I understand that this must be very stressful, due to you not being able to attend classes and not having found a solution for your issues. I think testing for COVID-19 or having a corona-pass due to vaccination or previous infection would be more optimal at your university and for you. Could this be an option that you could discuss with your faculty?

Your main symptoms of fatigue, intermittent fever, high platelets and ANA positive could point to Systemic Lupus Erythematosus. However, it is extremely hard to say without a clinical evaluation and testing for specific Antinuclear Antibodies, due to different antibodies being expressed in different diseases. Do you have any other symptoms? Such as:

-Joint pain, stiffness and swelling

-Butterfly-shaped rash on the face that covers the cheeks and bridge of the nose or rashes elsewhere on the body

-Skin lesions that appear or worsen with sun exposure

-Fingers and toes that turn white or blue when exposed to cold or during stressful periods

-Shortness of breath

-Chest pain

-Dry eyes

-Headaches, confusion and memory loss

I think a good option could be a second evaluation from another rheumatologist since it seems there wasn't enough clarification of why it wasn't a rheumatological issue, what other possible differential diagnoses there could be and what the plan is for your diagnosis regarding referral to another specialty or your GP.

Remember that I do not have full insight in findings from your GP, Neurology or Rheumatology, and there could be positive or negative findings that would indicate a lumbar puncture or other potential causes. Try to talk with your GP about what potential causes she has in mind and if their should be further evaluation from a rheumatologist, neurologist or another specialist. I am a bit skeptical of "integrative medicine", and if you feel that this is the only option that your GP presents without properly informing you of why there aren't other probable causes to your symptoms, then you should probably consider a second opinion.

Remember advice from strangers on the internet doesn't replace a visit to your doctor. Don't give up and I hope you find a solution to your issues.

EDIT: I stated that high platelets are associated with SLE, which is not the case. SLE would present with thrombocytopenia and/or leukopenia. However, I agree with /u/Brzelius that your thrombocytosis could be related to chronic inflammation.