Please post your thyroid test results and reference ranges so that members can assess the adequacy of your testing and treatment.
There are numerous references to the Hashi's related rash that you mention. this is a listing of some of them.
Two things that I have read that help. One is getting your thyroid hormone levels properly adjusted, which is why I asked for your test results. And two, is taking selenium as a supplement. Since selenium can be toxic in excessive amounts, you should get tested for selenium, to know what your level is, before considering supplements..