My story is this. The first round of golf I ever played was at the age of 18. I shot like 160 that day. 3 Years later I walked on and made the San Diego State University Golf Team.
So, I know it is possible. My background was wrestling and track and field. I never played baseball, so the whole swinging thing was new to me. My philosophy was simple. I would work just as hard at golf as I did as a wrestler. That's the hardest sport on earth so I believed that if I put in that type of work then I could make it. Plus I wouldn't be throwing up all the time. That was a huge bonus.
Also, I had no money so I never took lessons and couldn't pay to play everyday. I practiced my short game every day and didn't ever worry about how my swing looked. All I cared about was how I hit the ball, the shot shape and my short game. That's why today everybody calls me Mr. Short Game.
Long story but if you work hard you can make it on to a D1 college team.
Best of luck.