Vitiligo can be a symptom of celiacs (gluten intolerance) which is also an autoimmune disease. Celiacs can interfere with the absorbtion of nutrients as well as prescriptions drugs. Try to see if you have other celliac symptoms or try to avoid wheat products to see if it helps
Both are autoimmune disorders, meaning your immune system is attacking a part of your body. In the case of hashi, it's attaching your thyroid. I've read that if you have one auto-immune conidition, you're at higher risk to come down with another. Auto immune disorders usually have a genetic basis. I don't think the vitiligo is directly related to your thyroid problem, TSH, etc. This would be a good question to post to the MD on the MD forum. Also, tell your doctor!!