I can't advise you on supplementing with testosterone, hormone interaction is just too complicated for me. I supplemented with progesterone for quite some time. After I very recently upped my vitamin D (and A, and K2, als taking E) my need for progesterone was suddenly gone. Turns out you need vitamin D to make progesterone....
I try to give my body what it needs so it can rebalance itself: hormones and all. It's a difficult puzzle. One of my pieces was iodine. Another was definitely the fat soluble vitamins. My advise would be to try to find out what you are missing. (B-vitamins, B12, folate, minerals, fat solubles, protein, ...)
I know from Jeff T Bowles that vitamin D raises testosterone.
Quitting wheat also made a big difference for my allergies, fatigue, dry skin, abdominal pain, edema, big belly, bad immune system, brain fog, ....
As for Iodine
being responsible for low testosterone, I haven't had any bad reaction from taking iodine. Well, if you count detox, but that's temporary. I still take more than one gram daily. If I don't my thyroid starts working slower and slower. Every now and then I try what it's like on 100 mg or thereabouts, but it always fails.
Iodine does make everything work faster, so you'll need more nutrients. It does highlight deficiencies big time. During my first months of Iodine
I couldn't tolerate much iodine, I was so deficient in just about everything. When I took more than 100 mg of iodine, my heart would race, my head would pound. I felt like I would die. Now I know it was because of magnesium, potassium, zinc, etc deficiencies.