with throid problems you can get what appears to be the butterfly on the face but generally it is not red - the immune system upsets the way dead skin cells are shed - normally the average person drops skin cells on a continuous basis but hashimoto tends to upset that and you end up with dead cells building up roughly on the face and behind the ears you can see the shape of the butterfly on the cheeks with rough skin on the forehead and nose etc - there art several creams that can be used for this does not cure it however.I'm autoimmune thyroid, so that might tie in with what John salmon said about it
Just a word to the wise.............be aware that if you use a steroid cream on your skin daily, over time it will cause you worse problems than what you are using it for. I have known three people who ended up with systemic physical addiction to the steroid cream, meaning that it got into other systems of their bodies and started causing serious problems, but when they tried to stop using the cream the result was even worse. One person ended up in hospital and almost died from this. That person had been using the cream for years, so it's not always going to be that bad, but the other two had only been using it for less than a year and it took them each over a year to get clear of the consequences. Not everyone is going to have that serious of a problem, but I would never take the risk. The truth is, steroids are very damaging to the microbiome, the immune system, and to internal organs, and generally are to be avoided.I have fibro and rosacea. As johnsalmon said, I don’t there is a link between the two. There is inflammation with rosacea and my dermatologist gave me a topical steroid and it does help. Two things that make my rosacea worse is sun and alcohol.