Since you have hypertension and depression, it probably wouldn't hurt to have your hormones and thyroid levels tested, in addition to the CBC and other standard tests the dr will probably run. For the thyroid panel, ask to have your Free T3 and Free T4 run, as well as TSH. Quite often, your TSH can be well within normal range, but your other two levels could be out of whack. Most drs won't test the Free Ts so you do have to ask for it.
Good luck with your dr search and please keep us posted.