MWE,
Welcome!
When I hear about a symptom struggle a thyroid patient has, I always suggest that they ask their doctor to order thorough blood work up, if it has not already been done. I say this because if their is a co-morbid (co-existing) problem, it will usually affect other blood levels, such as in a CBC (Complete Blood Count) or the electrolyte levels (metabolic/chemical panel), etc..., which includes magnesium, potassium, calcium and sodium and phosphate. Electrolyte imbalances can not only point to another problem in the body but can cause symptoms of themselves.
There are things such as vitamin deficiencies that are also more common in thyroid patients, such as low B12 and D (both can be directly tested by blood) and both have potential to cause bone/muscle problems.
Another important thing, is making sure a doctor treats hypothyroidism adequately. Some in the medical community are angered when people like myself make the suggestion of checking up on your doctor by looking at lab retests that are done but the fact is, doctors have been known to under-treat or over-treat hypothyroidism. Doctors are not equal in treating different disorders and I feel it is ludicrous for patients to be expected to have an undoubting, blind faith in all doctors. I never say this to be offensive or to cast doubt on doctors as a whole because there are truly wonderful ones out there. I say it because like ALL PROFESSIONALS, there are those within them that do not represent their field of practice well and in fact in worse case scenarios, we refer to them as "quacks". This is term that is well-known and also why second-opinions have been around for as long as modern medicine has been.
I had previous doctors who actually told me that joint/muscle aches and weakness were not thyroid related! I then went online and found these symptoms listed for hypothyroidism and hyperthyroidism on practically every medical source I went to. I've also been told things like emotional symptoms are not thyroid related and I again found this to be a bogus statement after searching online. These type things are actually what drew me eventually into becoming a Thyroid Patient Advocate.
Anyway, if I may suggest as a starting point in advocating for your yourself in checking up on your treatment, I would obtain copies of your latest lab retests of your thyroid levels. If you're in the U.S., doctor offices & labs are obliged by law (HIPPA) to provide you these.
If you can get these or already have them, post the results here, along with reference ranges and we can comment on them. Your levels with treatment in my opinion are always an important place to start.