Hi Diana, I have this problem too. I have blocked pores and acne. When my face is wet it feels like sandpaper, even under my chin is rough. Taking Vit B12, Hydrocortisone and DHEA all have made the problem much worse. Whatever I do now I have pus filled spots.
The only thing that I have found that has softenened my skin is Nivea. I tried coconut oil too, and the next day the top layer of my skin rubbed off more than ever. My scalp is dry and flaking too, fore arms are so dry and rough I have little red spots all over them.
I'm trying to eat more good fats and have two fillets of salmon a week. This has helped get the rough spots off the top of my arms. Avocado and nuts are good too.
I have hashi's but my skin hasn't improved even on months of T3.
The corners of my mouth used to crack too. I think low B Vits can be a cause.
Drink more water to hydrate your skin, if I drink 3 litres the dryness improves.