Instead of going to the doctor and paying all that money, just take a quick trip to the school nurse and ask for advice. If she suggests you go to a doctor then it's probably serious.
It's okay to have irregular periods at your age. Playing sports, being under stress, and a lot of other things can factor in irregular periods.
By the time your 18 and older, if it's still irregular you should see a doctor.
I would have my period once every 4 months and it didn't get regular until I was about 18-19.
Your body is just trying to adjust to everything you're going through.