Thyroid auto-immune diseases are probably caused by elevated or high TSH in combination with selenium deficiency. I always suggest selenium use and multi-vits that list iodine+selenium. Please read the thyroid basics sticky. Note that higher amounts of iodine do increase TSH in a predicable and harmless manner, but that is often misunderstood. When taking higher amounts of iodine TSH lab results have no diagnostic value.
Normal T4 production creates a lot of free radicals that can cause damage if not cleaned up by specific enzymes that must have selenium in their structure. If that is not working, the immune system when cleaning up damaged cells and inflamed tissues can misread the cellular debris as foreign, then its an autoimmune state.
When iodized salt was introduced to populations, Hashi's shows up, partly because no-one was looking for it before in a sea full of goiters, lethargy and mental retardation. And the cases were probably there all ready, but the process was muted by not enough iodine for T4 production to generate free radicals.
Your maternal grandmother was on a salt restricted diet for high blood pressure that denied her of iodine [common]. Women have a greater need for iodine than men and also are more prone to hyperthyroidism and Hashi's etc.
Need AM temps [low] and mid-afternoon body temperatures.
Cholesterol is way too low. <160 is associated with increased all-cause mortality. Cholesterol is base for making sex hormones, DHEA, cortisol as well as Vit-D3.
If you have not been using iodized salt, doing thyroid labs may produce some interesting results, but the results will probably all be normal. If you get those labs done now, doc may easily refuse to do them again later.
Please see my prior list of labs.