Is TSH the only thing they're testing? They should also be testing Free T3 and Free T4, which are the actual thyroid hormones, while TSH is a pituitary hormone...
It's not the Hashimoto's that's causing your symptoms; it sounds like the problem is that the doctors are focused on TSH, only... If you have results for Free T3 and Free T4, please post them, with their reference ranges, as TSH doesn't begin to tell the whole story.
It takes 4-6 weeks for T4 med, such as synthroid to take effect, so I can't imagine your doctor switching your meds after only 2 weeks... Apparently, your doctors don't know a lot about managing thyroid conditions.