Welcome! First and foremost, really glad you got a new driver to enjoy! I use an R15 (the white driver that came after the SLDR). It's very similar and has the same sort of weights as your SLDR. It's a great customizable club. I love my driver (even though we aren't friends right at this moment). MrFlipper posted some great info of course on that, so be sure you take a look.
Second, nice swing -- already. It's easy to see that you have a lot of talent. The instruction you'll get here is great and the folks are really nice, too, so we hope you stick around.
I'll post a few things about your swing, but full disclaimer I don't do golf instruction for a living so you can pick and choose what you'd like to read. And funny that actually you have the same stuff in your swing that I am fighting right now too (though you are obviously compensating better, lol).
Not sure how terminology familiar you are here so forgive me if I am preaching to you something you're already aware of. And another thing to note -- if I post pictures or something of tour players (really, anyone who does) isn't doing so necessarily for you to copy exactly, but just to show you what along the lines it should look like.
Something you will want in your swing is called secondary-axis tilt, or SAT. What it is is a little tilt away from the target at your setup. You will maintain this tilt throughout your backswing into impact (the best players in the world even increase the amount of tilt they have in transition -- but that's a different topic.) It's a little hard to tell from the camera angle but it looks like your spine is set up quite vertically to the ball, and especially with a driver you'll want to be away from it.
Bubba Watson has a great driver set up in terms of tilt away from the target. With the magic of photoshop, I flipped him to be right handed here. Because your bottom hand on the club is lower than your other hand and arm, your trail (in your case, right) shoulder is going to be set lower too; therefore, your body ought to have some tilt as well. See Bubba's shoulder line and how his spine is tilted here. There's a lot of good things this tilt will do for your swing and physical wellbeing, but in general it's a good thing to have. (ignore his ball position because it's a little unusual [further back] for a stock driver swing. Bubba gets away with really weird stuff the rest of us can't.)
Next, your arms and hands are overrunning your turn in your swing. This can be a power leak and lead to general inconsistency in trying to deliver the club back to the ball. You're also an extremely flexible person so it's probably going to feel "powerless" stopping shorter.
However, take note here in the capture from your swing video how in relation to your chin, the dark line on your shirt hasn't moved any further back. (I also lightened the photo a bit) This could also be contributing to your right shots -- when your right arm disappears behind you like that, you have no choice but to reroute it back in front of you to wipe across the ball, which would cause it to go right.
You have a nice turn as it is. Take these photos as a guideline and not a "this is where you have to stop" -- just wanting to show that your arms overrun a little bit. Also, the further that you go back with your swing, the more clubhead speed you're required to have to get it back to impact. I superimposed two images of your swing on each other, and you can see your body is the same position but your club has traveled a lot farther. From what your mother has told us, you swing pretty dang fast already, but the position that your clubhead gets to in the top of your swing is really a 120+ MPH position, and even for people who do swing that fast isn't always ideal. Have you ever seen JB Holmes? Take a youtube search for his driver swing and see how far he takes the clubhead back, and he is one of the fastest swing speed players and longest drivers on the PGA Tour. The key will be, as you will discover the more you practice and play, is knowing where your swing ought to stop so you can get maximum consistency and acceleration.
Hard to say with just a driver if it's a driver thing or other clubs, but your shoulder turn also looks a little flat on the backswing, which isn't an ideal position to be in either. Pause at the top of your backswing, and pretend you drew a line right across the top of your shoulders through your neck. Your shoulders would be pointing out into the trees whereas preferably you'd like it a little more pointing toward the ball. When you have a flat shoulder turn your options will be either to dump your right shoulder to the ground on the way through to stop from getting steep, or to actually get steep and wipe across it which would again cause a right side miss.
Lastly, a small question and a bit of just general playing advice for you.
When you say "fade" do you mean an actual fade (starts slightly left of target and ends slightly right of target) or a slice (starts left or even right of target and curves WAY right of target). If you mean an actual fade and it's still a nice shape of curve, I wouldn't mess with it too much. Of course, you don't want to be banana curve slicing it either, but because you are young you will find lots of people coming up to you on driving ranges wanting to give you advice. Something you may come across from a person at some point or another will be that a draw is a "pro's shot shape" -- which is not true. Many PGA tour players favor fades over draws and are very successful with it. Fade VS draw is not the key to good golf.
Of course, as you get more practiced you'll want to be able to work the golf ball both ways and different curves -- and that's fine. But what you'll also want is knowledge of what your "stock" swing does so you can go back to it under pressure. As they say there's not pictures on scorecards so there's an infinite number of ways to get the number done.
I say this as a word of warning -- a fellow teammate on my university club team did himself no favors by insisting to himself that a draw was the way to go ALL the time and it was the only way that he could play successful golf. A slice, while certainly not pretty or ideal, is, in general, more manageable a miss than a nasty snap hook left that you'll never see again.This is why I am proud of my fade and never let anyone tell me otherwise!
Here's how things break down for my club team:
There are 10-ish of us total
2 of the guys can work a ball either way at will and do so often (they are the best players on the team)
3 of the guys play draws and can fade it if need be
2 of the guys play fades and can draw it if absolutely needed (this is where I am, if my life depended on it, lol.)
3 of the guys play draws and couldn't hit a fade if their life depended on it
and 2 play fades and couldn't hit a draw if they had to.
The need be, for me, is hitting a draw on the course maybe 2 or 3 shots per round. It really isn't often. Unless there's a significant dogleg left hole or something I'd like to go for (say there's REALLY bad trouble right but it's OK to miss left - I'll try and hit a draw). My draws usually actually draw a little bit or just go straight with no fade. But you'll want to find your shape.
If you want to be successful at golf, you should learn how to at least do both and practice as needed. However, the moral of that little story was simply to tell you that it's not life or death if you have one shape or another, and the other point of the story was don't buy into random driving range advice.
And finally, just a word of encouragement: Kudos to you for going at golf and learning so much on your own. That's really awesome. My university's club team goes to local high school and middle schools to show students what college golf can look like, and that it isn't always playing for Ivy League schools and shooting under par. It can also be a good time to hang out with friends. Keep golfing, no matter your goals or where golf ends up taking you. It's a very frustrating game at times, but it's very rewarding and I'm thankful for all the opportunities that golf has given me.
Kudos to you if you stuck with my post and actually read all of that, haha! Hope some of the advice helps - you have a good swing to start building on already! Keep us all updated on how tryouts for your high school team go, and hope to see you posting around with progress updates. Let us know if you have any questions