I have had folliculitis in the past, but I don't believe it is related to MAI. Here is what Cleveland Clinic has to say about folliculitis:
https://my.clevelandclinic.org/health/diseases/17692-folliculitis
Bad you mentioned Hashimoto's as well, and there are a number of skin conditions associated with low thyroid, including itching, rash, hives and in some cases folliculitis.
Maybe you should contact your primary or whoever is helping manage your Hashimoto's to find out if your meds need to be adjusted.
Sue