97 Sunfire Transmission Problems

PLEASE HELP!!! I hope some one will be able to help me on this, My 16 yr old daughter just bought her first car (97 sunfire 2.2 automotic tranny) And it now has a problem. The transmission doesnt seem to want to shift. It shifts out of first just fine, at normal speed and rpm's but then it doesnt seem to want to shift, I couldnt tell if it went into second gear, since the engine was revving to 4000 rpm's at 45-50 mph and I didnt dare to try to push it any harder, but if I put the car manualy into 2 then the rpm's would drop for a second and go right back up. THe fluid level checked ok, but had kind of a burnt smell, and the engine seems to be running good. Any info would be of great help since she spent her whole saving to buy her first car and I will be the one paying the repair bill, if its worth fixing.