First treat the hypo!!
My total cholesterol was 237 last year with a TSH between 3.5 and a high of 6. I was finally diagnosed.
My TSH is now 1.2 and my cholesterol is.....drumroll.........183.
No change is exercise or diet. My previous PCP (not the word previous) was not going to treat my thyroid unless my TSH was over 10, but he was happy to suggest a statin for the cholesterol.
I agree with estrinha.
Hypothyroidism causes high cholesterol. Your TSH result is high and indicates you are hypothyroid.
I would not take any cholesterol medication until the thyroid issue has been explored. If you have hypothyroidism and that is treated, your cholesterol will probably correct itself.
The first sign I had of a thyroid problem was high cholesterol.
Hypothyroidism can be responsible for high cholestrol , not the opposite, You should go first to a Endo and check for TSH (again), free T4, free T3 and for thyroid antibodies (TPO and anti-Tg), your TSH is high, do you have other symptoms?
Perhaps the ENDO will give you levothyroxin to lower your TSH. First you should treat what is causing your high cholesterol...