Iodine is a natural mineral, essential to life. Finasteride is a synthetic androgen inhibitor.
If I had to choose between ingesting a natural mineral or a synthetic androgen inhibitor, I would think about it for a little while.
I'd also look very carefully at diet and other habits, other drugs taken, mineral deficiencies. It is a huge endeavor to determine what's going on. The harder part comes later when the person attempts to initiate changes in habit.
I wouldn't say Iodine causes hair to fall out, I still have mine, In most people, Iodine doesn't cause their hair to falling out. What we do see is that Iodine causes toxins present in the body to be eliminated.
I'd suggest that you will likely never figure this out on your own, and most endocrinologists aren't up to speed with reality, so you need a special coach.
Remember, vitamin B-12 is biologically active at a concentration of one part per trillion. What's in your drinking water ? Do you eat commercial wheat products ? Oats ? How much glyphosate is detectable in your urine ? What was your mercury exposure like ? Do you take flu shots ? Do you ingest artificially colored foods ? How much BVO's have you consumed ? Theres a hundred more questions