Let me preface this by stating that I do not know your full situation.
If I am correct;
You have been diagnosed with hypothyroidism. After seeing a doctor, it has been determined that medication is not helping the situation.
With that caveat. your hypothyroidism is uncontrolled, whether you feel better or not is irrelevant. Your diagnosis and medication not helping is the issue.
From the Medical manual
(1) Current goiter (240) is disqualifying.
(2) Current hypothyroidism (244) uncontrolled by medication is
(3) Current or history of hyperthyroidism (242.9) is disqualifying.
(4) Current thyroiditis (245) is disqualifying.
From what I am reading regarding your post you are at a dead end. The fact that you feel basic would not be a problem is moot. The issue is at anytime during your career you could have a major issue and not be near medical help.
I wish you the best of luck in your future endeavors.