You CAN do it. Just like anything else practice, practice, practice. Glad to hear you have a teacher/coach

I have swam since I was 5 years old, advanced to instructing and lifeguarding then 5 seasons ago our HS girls swim coach started offering adult workouts. After 30 years I had to totally learn how to swim again. (well almost totally - i could still float, albeit gasping for air)

for 3 months I did nothing but laps and laps of practice drills without ever really doing the full stroke. When I finally did put it together I was WAAYYY faster and more efficient than ever.

The not so fun drill and technique laps are really worth it.