I would refrain from thyroid supplementation until you figure out why calcium is high. Depending on the cause, thyroid may make things worse. Ray said that aspirin is helpful in hypercalcemia but he did not elaborate if aspirin lowers serum calcium directly or protects against the toxic effects of high calcium.
I'm curious why you mention staying away from thyroid while calcium is high. I have high-ish calcium (10.0), low magnesium (1.7 serum/4.9 RBC), elevated PTH (41 pg/mL), and for the past couple years I've been using T3, now Tyromix. I wake up every morning with whole body spasms and the feeling of my GI tract vibrating like a cell phone, until it becomes painful and then I either feel nauseated or vomit. I haven't believed the thyroid to be at fault, because my temps and pulse are still low.