Patchy hair loss

Hi everyone,
I was wondering if anyone had advice, I’ve been to a dermatologist who didn’t really offer much.
I have a patch at the front of my hairline, about 2 inches wide and an inch
deep, that isn’t completely bald but definitely very sparse. I also feel like my part seems to be thinning, in the front half. The back half is fine, and if I
part on the other side (where I normally don’t part,)it’s fine. I measured the difference in parts and it’s about a quarter inch, so definitely a difference. I have parted on this side for a few years because of a cowlick on the other side, but I’m going to switch now because I’m so paranoid about my widening part.
I have had low ferritin (now it’s up to 16 after being at 7 but 16 seems really low still), am taking iron
supplements (slow Fe). I also seem to have had thyroiditis, because I was mildly hyperthyroid for several months (subclinical, my doctor says). Recent bloodwork shows the thyroiditis has resolved itself. The dermatologist
tried one set of steroid injections, which didn’t cause anything to grow (but I
don’t know if one time would do that much?). I also tried Rogaine, which caused a terrible rash after 3 days.
Because it’s so patchy, the dermatologist thought it was androgenetic alopecia (although there is mild thinning elsewhere). But I’m also worried about the thinning part on the one side-does hair usually thin in patches, so along the area where you part the most? My hair looks bizarre when parted in the middle because the part is normal until you reach the front where there is a big balding portion!
Does anyone know how long it would take for regrowth if the problem was due to
low ferritin and/or thyroiditis (the thyroiditis has corrected itself now, but
I’m not sure where my ferritin should be for good regrowth)?

I’ve not noticed my hair falling out in large amounts until the past couple days (after I tried the rogaine for 3 days).

Thanks!