Have you been to a Rheumatologist yet. They would be more able to help you figure out which autoimmune dx you may have.
Yes, they can all be related. I have had worsening POTS for years. Finally went to Cleveland Clinic where I ended up being diagnosed with Small Fiber Neuropathy, a form of peripheral neuropathy. MedHelp has good info in the Health Topics under Peripheral Neuropathy. Your small fiber nerves control your autonomic functions (BP, heart rate, sweating, breathing, etc.; anything you don't have to think to do). They also control feeling and some fine muscle control. So there's all those symptoms. There are a lot of things that can cause peripheral neuropathies. In my case, Sjogren's is the autoimmune disease that got my system started on destroying the nerves. If you do some reading on Sjogren's, you'll find that it can cause small lesions on the brain and in some instances mess with your thyroid. I would suggest going to Sjogren's Syndrome Foundation and Sjogren's World (SW has particular articles about neurological involvement). It's also possible you have an autoimmune disease like Grave's or Hashimoto's, which are particular to the thyroid. Most of all, it sounds like you need new doctors if that's possible.