How to improve my climbing?
Too much info for a comment, I've checked the suggested duplicate and this is slightly different.  This question is about effort and approach, not climbing technique.



Answer You're going at the hill too hard.  Learn to PACE your efforts.

Medical rule of thumb, your maximum heart rate should be 220 minus your age.  I'm 40 so my heart rate should not exceed 180.  However my HRM in strava shows peaks in the high 170s.
So 200 BPM might be a maximum heart rate for a fit 20 year old.

If you're doing decent flat speeds, then don't expect to travel uphill at those same speeds.  I think you're trying to keep the same speed and blowing yourself up.

Instead, find a quiet grade of about 8%, and start by riding up like normal.  Note how high you get before you have to stop.  Then turn around and go down, resting and recovering.

Second time - go up the hill in your bottom gear (that's the small front and the biggest rear cog)  Focus on keeping your pedalling cadence at "normal" and avoid pedalling too fast.  Also avoid bouncing in the saddle, but stay seated.  You will ride slower, but see how high you get before you have to stop.  I bet it takes much longer, but you will well exceed the turnpoint of the first attempt.  And you'll be less shattered passing that point too.

Climbing is all about PACING your effort.