It would be rare for thyroid replacement medication to cause this (assuming you are referring to levothyroxine). It may be difficult to find an answer to these questions.
Often people with one autoimmune disease develop others. The rashy type pimples that itch and scar perhaps is dermatitis herpetiformis. I went six years before being diagnosed. They usually occur symetrically (on both sides) on the elbows, buttocks, knees. I have had bad outbreaks where they occur down my spine (due to a shampoo), on both earlobes, eyelids, both shoulders. They look like blisters and itch incredibly until you scratch them open. Sometimes they'll fill up again. They release a clear-to-yellowish fluid when scratched open. If these signs sound familiar to you, you should know that dermatitis herpetiformis is related to celiac sprue. It is an autoimmune disease triggered by ingestion of gluten (protein in wheat, rye, barley, and possibly oats). Your body basically attacks itself wherever it finds the gluten. Of course point of entry is the intestinal villi, so these become flattened and can't absorb nutrients correctly causing a host of issues. Additionally, various body systems can be affected as the body attacks parts of itself. The symptoms are very varied. Unfortunately, most doctors don't even really know about it, although research knowledge has exploded over the last few years. They are finding 1 in 133 people are probably affected. Although it is genetic, it often doesn't come to light for years. Experts say otherwise, but using shampoo with hydolyzed wheat protein even caused symptoms for me. Also, my baby daughter has reactions from my breast milk when I eat gluten--even though they say it is impossible. It is important to note that you might not feel any intestinal symptoms. I don't usually when I eat incorrectly, however, it still damages your intestines. The only treatment for celiac sprue is a gluten-free diet. Sometimes dermatitis herpetiformis seems to have pop-up occurrences for me. These pop-ups are treated with dapsone. I take a 25 mg tablet or two and everything goes away. (Suggested treatment recommends daily intake, however my doctor and I haven't found that necessary.) It was truly a miracle drug in my life when first diagnosed. A simple skin biopsy can confirm dermatitis herpetiformis and many different tests can be used for celiac sprue. However, if you have dh, you DO HAVE celiac sprue for sure.
Hopefully this helps, maybe your skin symptoms aren't what I described though.