Your thyroid numbers do -not- indicate any thyroid issues. Yeah, your TSH is a bit on the high side, but it's still in range. Can thyroid issues trigger libido issues too? Yes! In your case though, I seriously doubt it.
In my case, I have Hashimotos. At one point, FT4 and FT3 were in the dirt and TSH was around 27. It took me almost 5 years and 4 docs to finally get it all under control. Now my FT4/FT3 are in the upper high of in range and my TSH is at a comfortable 0.8. This was a major contributor to my "issues". Once I had that settled, THEN I could focus on TRT (I'm 60 by the way). Once I had this under control, libido issues subsided.
Oh, and TRT can also be over-done! I've found that I feel my best when I keep free-T in the upper 1/3 of in range and my E2 is around 25-ish.
I've tried iodine in the past too. Was using Lugol's Solution. I'd add a few drops to some orange juice in the morning. Boy howdy, that brings on some good energy...but it can be over-done! I found that if I took too much iodine, I would get stuffy. I had energy but still felt like sxit. Now? Just 4 to 5 drops of Lugol's in some orange juice a few times of week seems to work best for me. Iodine can and will affect thyroid function.