Hi Gracevd70,
I'm sorry you're experiencing muscle weakness... I am not a doctor, but I just did a little googling because I know muscle weakness in the shoulders and thighs can sometimes be associated with hypothyroidism, and it looks like autoimmune diseases like Hashimoto's and Graves, as well as both hypothyroidism and hyperthyroidism can all cause muscle weakness.
The short answer is that all of the above - hypothyroidism, hyperthyroidism, or other can all cause muscle weakness. Muscle weakness in the muscles you are talking about feeling weakness in, like from pushups (triceps, deltoids, maybe biceps and trapezius) are associated with hypo and hyperthyroidism though, so I think you're on the right track to look in to your thyroid hormone level as a cause, but I can't say it is definitely one of those, or which one it is.
One hypothyroidism symptom is "frozen shoulder", where you can have weakened muscles in the shoulder and arms, pain or general achiness in the muscles, muscle cramps, loss of grip strength, joint pain, pain and weakness in the muscles worsening with cold temperatures, and difficulty raising the arms over the head. (I have Hashimoto's, and have had both shoulder pain/weakness as well as muscle weakness in the front of my thighs at a time when I was experiencing a lot of other hypo symptoms).
Graves disease and hyperthyroidism often cause muscle weakness and fatigue, but pain is not as common as with hypothyroidism. From the website I'm looking at (on "thyroid info", I googled "hypothyroidism shoulder weakness"):
"Some people with hyperthyroidism actually lose muscle tone and strength, a process that can be referred to as "muscle wasting." Some common complaints include:
difficulty climbing stairs
difficulty holding or gripping objects with hands
difficult reaching arms above the head "
My thoughts - lots of things cause muscle weakness and it could be unrelated to your thyroid hormone levels, but weakness especially in the arms and shoulder is both a hypo and hyper symptom, so that is a good place to start looking for a cause.
I would talk to a doctor about it and make sure you are at the right level of hormone treatment. Are you having other hypo or hyper symptoms? I would guess if you are experiencing muscle weakness from being hypo or hyper, you would likely be experiencing other symptoms as well. I know sometimes with thyroid cancer treatment they aim to get your TSH as low as possible to suppress cancer growth, below what might be "normal", which might cause you to have more hyper symptoms, but this depends on the individual and your personal cancer treatment - in my case I think we are just trying to get my TSH down to a "normal" level following my thyroidectomy for thyroid cancer.