Yes it is very likely, as the calcium is actually absorbed out of the bones, and deposited into the blood circulation, causing bone pain and possibly other symptoms as well.
The only treatment for this is surgery. Your bone density come back positive for calcium loss/low density/osteoporosis if your GP's diagnosis is correct.
Once this is confirmed you need to start "shopping " for a very reputable
endocrine surgeon who has a lot of experience in these procedures,
to perform a minimally invasive surgery to remove the tumorous parathyroid gland- you have four, don't worry. Some people have two removed, which is more rare.It's a fairly safe and fast operation and if you're in good hands you'll be sent home within a few hours.
It's on e of the conditions with an extremely high cure rate and very few issues afterwards. Just make sure you select the "right" surgeon.
I am not a doctor, however, I understand that hyperparathyroidism can result in calcium being removed from the bones. This will in turn elevate your blood calcium levels. Most people have four parathyroid glands. They are very tiny and located in the throat where the thyroid gland is located.
Hyperparathyroidism can be caused by one of the parathyroid glands developing a tumor. If this is the case, removal of the one parathyroid gland can solve the problem, and parathyroid function will most likely return to normal. Left untreated your bone density will become thin, thus the reason for a bone density scan. I do not know if the arm pain is related or not.