I'm a gymnastics teacher, and I've dealt with my own pains as well as those that my daughter might get.
A muscle strain usually happens when the gymnast is attempting to do a trick that she is not strong enough for. The muscles can't take it and then small tears appear in the muscle fiber. Now, the good news is that this is how muscles work, and that having a sore muscle means that when the muscle heals it will be stronger. That's why we get sore muscles when we work out. It's also due to a build up of lactic acid in the muscles.
I would venture a guess that back pain is probably from doing bars. Many gymnasts don't have very strong stomach muscles so they use their back muscles instead. Strengthening her stomach muscles will help.
As far as muscle strains go, ice the area and use ibuprofen until the pain goes away. When the pain is gone, then she is FINE!! She should just ease back into the activity, making sure to warm up and stretch properly.
I wouldn't keep my daughter out of gymnastics if the pain was gone! And if you're going to be in gymnastics, expect lots of sore muscles, sore backs, sore knees, sore ankles, bumps and bruises.
Also, doctors aren't very good with sports injuries. They just recommend you stop the activity for a week. You'd need to go to a chiro or a sports specialist to get a better diagnosis and treatment.
I would bring your daughter to class and explain what happened. If the instructor is good, she will give your daughter extra help and keep an eye on her. Your daughter should be instructed to stop and tell the teacher immediately if she feels any pain.
Kids come to my class all the time with injured muscles, hurt ankles, etc. They are eager to participate and we just go gently with them and help them do the things they can do.
Your daughter needs to STRENGTHEN her muscles, not stay away from class! If her back hurts, then the rehab would be to work on her abs.
Good luck!