Do Psychiatric Meds and TRT Mix?

Your TSH is very high, ideal should be close to 1.0, you are likely iodine deficient, please check thyroids basics stick: Thyroid Basics Explained

Buy two or three thermometers and checks temps waking up and on mid afternoon. Put thermometers bellow tongue, not on armpit.
Waking up should be > 97.3 F. >= 97.7 F is ideal.
Mid afternoon should be >= 98.6.

Do this for a few days, if your numbers are off, you likely have sub-clinical hypothyroidism. Most common case is iodine deficiency, in that case you can get your hands on Iodoral to boost your levels. Read the link for more info, KSman goes in much more detail.

From my experience with psychiatrist, it is like that old saying “when you have a hammer in your hand everything looks like a nail”. They will look at your problems and just prescribe meds and more meds, without looking at the root cause. And more often than not, meds create more problems than they solve.

Your T is very low, and it is not unlikely your mind problems are related to that. You should consider TRT, but before that, read as much as you can from this forum to make a informed choice.