School can be one of the nastier places for younger trans folks who either haven't been living stealth or able to transition at all. Is that one counselor you saw the only one you're able to speak to? I ask because some schools have multiple counselors, or even a legit psychologist available to their students. My former high school had a psychologist(but she was more or less in charge of special ed, as far as I know), a few different counselors who could help you with classes and planning, and then there was one lady who worked at an office in the next county over who had an anxiety support group.
Of course, your resources could be different. Maybe you should try to educate your parents in that while a "sex change" may not make you HAPPY, it may help treat the depression and problems that come with gender-related dysphoria. Basically like you're treating any other condition that affects your well-being. Treating it could involve therapy, hormones, surgery, etc. All the things you know, but said in a way that might open them up to at least supporting you by bringing you to a therapist who can help you deal with the problems at school.
They might not want to talk about it, but that's like not wanting to face the truth. You have gender issues, you want treatment. As your parents, they might think ignoring the issue is what's best for you(probably because they don't understand and don't know what to do with you), while that's not the case.
Be patient, but try talking to them about this calmly. I know it's hard to be calm, given the circumstances, but people tend to take things better if the other party is able to speak maturely and in a level manner. If your mom is the "burn everything different because SINNERS" type, try looking up a support group for Christian parents and print off some information to share with her. I'm not a religious type at all, but surely God would want you to do what you feel is best for your mental and physical well-being, right? Blah blah blah, you were made this way for a reason, and that's not your mother's call to determine why you're like this and what you should do with your body when you are an adult. Imo, I feel like you should at least have a supportive therapist who can help you. Your parents shouldn't deny you that.
Does your school offer an alternative to PE? PE is important and all, but if you can't bring yourself to dress out due to dysphoria, surely there must be another option for you and other people who cannot participate in the class.
And, failing that, have you tried just wearing sweats instead of regular pants on your PE days? You can just go into a bathroom stall and change out your shirt, and with colder weather coming up, sweats make more sense than shorts. I'm guessing your school has a specific shirt or something they want you to wear, and I'd just roll with it and put it on. You shouldn't have to dress out in front of other people if you don't want to. :/ I always thought that sort of thing was borderline abusive. Being in a state of undress around others is one of the most uncomfortable things I can think of putting a younger person through.
As for the girl, you don't have to talk to her or answer her questions if you don't want to. It may seem rude or whatever, but you're not her therapist. You don't have to baby her and take care of her. That's not your problem. If she continues to bother you, tell her to back off. Or if you would prefer being polite, just say "I'm sorry, but I don't think I'm capable of answering your question/helping you/etc."
All in all, I feel for you. School is awful, at least in the social aspect of things.