Floating f, reading between the lines, it sounds like you may have previously undiagnosed asthma,and it sounds like exercise is a trigger factor. I can't think of any other obvious causes in an otherwise fit 28yr old.
Peak flow rates can be variable, and to some extent, rely on technique. Practice can "help" your readings,but spirometry is less easy to manipulate.
Your height shouldn't be an issue, as the reference ranges used will take this into account.
Generally,lung function can be improved with exercise, but in your case, things could initially be made worse.
I suspect that you symptoms will improve with continued inhaled treatment.
The good news is, that from previous postings on this forum, pilots seem to be able to fly with controlled asthma.
Keep us informed, and let us know when you get your ticket.