I think there's a way to create a Game Golf account without owning the device. You can then recreate your round in their system (if you're like me and can still remember shot-by-shot a few hours later), and get a "strokes gained" analysis. If you hit 11 greens, there's a good chance that yes, short and mid irons are a strength of your game (approach shots in general are one of mine, and my tee shots don't go anywhere near as far as yours do, not even on holiday). Of course, one round is a small sample size.
Also, good on you for all the practice you're doing. Consider participating in this site's "5 minutes a day [minimum]" challenge. It's a good way to keep with the practice and improving.
For making longer putts... consider doing one of my favorite drills. After some warm-up, set up 12 markers on a practice green 5-6' from the cup, roughly equally spaced, like the numbers on an analog clock. Putt from each in turn; when you make a putt from a marker, pick it up. If you miss, go to the next marker (but leave the marker you just missed from in place). Count how many total putts it takes you to do this.
Golfers who shoot in the low 90s (which is probably around the putting skill you and I have) average making about 50% of their 5-foot putts and just under 40% of their 6-foot putts. So, from 5', taking 24 putts to finish would be good for that level, and 30 putts from 6'. Obviously, we want to improve those numbers, but recognize there's a ceiling: scratch golfers tend to make about two-thirds of their 5' attempts and about 55% of their 6', so expecting to get 5' under 18 or 6' under 22 would be a stretch (unless your putting becomes an outsized edge... in which case, you're spent too much time practicing putting, go hit some drivers and irons).
(These average numbers from that distance are from Every Shot Counts, page 55, if anyone wants to fact check me)
What should that drill help you with: if you can make 1-2 more per round from outside 3', even if it's just from 5-6', you'll improve a bit, probably in the form of turning a 3-putt into a 2-putt somewhere.
Lastly, next time you play that same course: consider your tee shots. The three shots that went beyond missing the fairway and ended up in trouble (woods / lost ball), check if there's a better place to aim or miss on that hole to keep your driver shot in play. If there isn't, that's when you want to move down to a lower club.
So guys I have an update. For the past week and a half I have gone to the putting green every day and practiced my putting and chipping for a little over an hour. I hit a bucket twice in that time. Today I shot my new personal best of an 81 at a par 71 course from the whites (69.4/129).
1 putts: 5
2 putts: 10
3 putts: 3
Other takeaways today:
- Five 1-putts and only three 3-putts for me is excellent. I would attribute this to making all of my 2-3 foot putts this round except for one on the back. That said, my chipping was relatively good today, setting up roughly five 1-putt opportunities all of which I converted on.
- I still did not make a single putt today outside three feet. Realistically I think this should happen once or twice a round so I think there is still work to be done on my putting.
- Despite hitting only 7/13 fairways I managed to hit 11 greens. I hit driver 11 times today. 10 of which landed 280 yards or more from the tees but 4 of which did not hit fairway. 3 drives put me in the deep rough or woods. 1 ball was lost today. This leads me to believe my mid-short iron parts of my game are strengths, driving is so-so, chipping is so-so and putting is still poor to average.