What sport can an unfit, fat girl do in high school?

Swimming is a good as a way to ease yourself into sport because it is very low impact, but really the important thing is to find something you enjoy doing.

If your breast hurt to run then it means you are not wearing a well fitting supportive sports bra. I wear a 30F/28FF depending on style/brand and I can comfortably run, trampoline, and do gymnastics and aerobics when wearing a sports bra. The sports bras I have found best are The Freya Active Moulded Crop Top Sports Bra http://www.freyalingerie.com/lingerie/activecroptopsportsbra/ss14/moulded_crop_top_sports_bra.aspx?colour=electric%20black and the Panache Sports Brahttp://www.panache-lingerie.com/au/products/details/panache-sport/sports-bra/a/a both of which are underwired and moulded with a racer back and offer both encapsulation and compression. To work effectively any bra needs to fit properly and there is good advice on that here:
http://sameatschildren.tumblr.com/post/45962915522/do-it-now-guide-to-proper-bra-fit-and-measuring
http://www.bravissimo.com/perfectfit/
http://www.figleaves.com/uk/fitting-room/bra-calculator/?link=lingerie_tn_bracalc

Walking 4 calories per minute, 400 calories in a burger

Golf? Perhaps... water polo?

pingpong

Water Skiing
Table Tennis
Track and Field: Weights
Canoe/Kayak
Horse Racing
Golf
Cheerleading
Roller Skating
Equestrian
Archery
Curling
Bowling
Shooting
Billiards
Fishing

Any.

Dont sell yourself short, you can do anything you want.. will it be hard? yes but totally worth it.
I agree with the water sports comments. Best of luck,

think about water sports as in water polo.

You could be a shot putter.

Idk