Hi! and welcome,
I am a mom, gram, and old pediatric nurse. I agree that you need to see a pediatric rheumatologist asap. If you are near a major teaching hospital, thats where I would start. I can't give medical advice, but if you were my family, this is my advice. Listen to your instincts and advocate loudly for your child. Ask your family dr. who they would send their own child to see. Autoimmune illness is hard to diagnose on a good day. Type up a timeline of her complaints and symptoms. Keep a diary of anything that might be a trigger for her, foods, activity, sleep patterns. Ask every dr you have already taken her to see to give you copies of anything in her medical record that might offer a clue to what is wrong. They may charge you for copy costs, or require you to sign or send a written request. Don't give up. Remember, that a good medical practice will be happy to help you through this. And if your child is that distressed by gym class, maybe you could make an appt. to see the gym teacher and the school nurse together. They would be excellent resources for you, I am certain they have your child's best interest at heart. There might be a compromise for your daughter to not participate in the regular class, at least pending the pediatric specialist's appt. If necessary, ask for an evaluation by the Committee on Special Education. The team might help identify any clues in her behaviors, and evaluate any possible emotional distress issues, even share their insights into or evaluation of any possible pain or bullying issues. I only know the law in New York State, but you could research your school, or ask to speak to the school psychologist for clues to where to start in your state. Here, if one is requested, the process for an evaluation must be started per state education law. I know how children can hate PE, I remember how I did.Because she is so stressed by her PE class, I might be tempted to let her skip gym, I think the requirements vary by state. Maybe a compromise with her until you could meet with her gym teacher. Don't hesitate to use your daughter's principal as a resource, too. I am a retired teacher, and I know how busy they are, but your child is THEIR job. A word from an effective Principal can muster a team meeting of your daughter's teachers in an afternoon or two. And sit down with your child/siblings/family and involve them in this process. Pick a best time to ask your daughter what she thinks, and what she wants, and share your plan with her. Kids are really good at picking up the fear and worry of the adults around them, way more than adults might realize. And needlesticks or injections are tough on kids of any age. Arm yourself with knowledge and questions. Write a list of what you want to ask the specialist, what your goal is, and what you want him/her to do for your child. Drs. love to have new patients come to the first appt. with a simple, edited, written history of the illness, with complaints identified in priority order. Hand the dr. a copy to scan, (trust me, drs. read FAST 
) when you first get there. And take a notebook and a pen in with you! Write notes as best you can. Hand the notebook over before you leave and ask him to write down the plan/preliminary diagnosis/ the rule out issures, and worry about her handwriting later. I am glad you found this forum, there are many threads filled with advice that comes from firsthand experience by many. God Bless and keep us posted,
suetoo