I presume you are on a gluten free diet due to the Celiac. I just wanted to find out if you are being adequately treated for the consequences of the Hashi's, since that seems to be the exception. You certainly have some symptoms that are often associated with Hashi's. What do your thyroid related test results look like, along with reference ranges shown on the lab report? Also, if tested for Vitamin D, B12 and ferritin, please post those as well.
Rheumatoid Arthritis, Celiac Disease, Lupus, and others
Go to any website, WebMD, Thyroid disease manager, etc. and search it, they will tell you everything.
Yes, your immune system keeps attacking your thyroid until it does not function at all. At that time you are on total hormone replacement for the rest of your life.
You're also right that once you have one, you are more likely to develop another. The list includes (but is not limited to) lupus, rheumatoid arthritis, celiac disease (gluten intolerance), fibromyalgia, etc.
Hashi's is the most prevalent cause of hypothyroidism in the U.S. So, there are lots of us out there. Welcome to the group!