1) When I recommend closely examining your diet I didn't mean to suggest you are gluten intolerant. Diet and its impact on health are profound. A skewed diet can, in the long term, cause a whole host of strange issues. Gluten sensitivity, which seems to have caught the media's attention, is just one example of a dietary issue. All I am saying is take a long hard look at your diet, especially if you have any digestion irregularities.
2) TSH alone is not a good indicator of hypothyroidism. Having said this, TSH=2 is really very normal (although perhaps not ideal) ... especially for a man. Men generally run asymptomic until you get a TSH above 5 whereas women sometimes suffer with values well within the normal range. And so I have skepticism as to whether you are hypothyroid ... unless your free T3 and free T4 are low or low-normal.
3) There is certainly a strong hereditary aspect to Hashimoto's. But if you don't have antithyroid antibodies then, well, you simply don't have that autoimmune disease (..yet).
4) Losing one's body hair over a long period of time is certainly not normal. It is good you are researching the cause since this symptom might be a harbinger of worse things to come unless you nip the problem in the bud.
Oh and since this is an Iodine support forum, supplementing with Iodine (and co-requisite supplements) probably can't hurt since most everyone is Iodine deficient to some extent. However personally I would look more to fundamental aspects of your diet(, lifestyle) for clues and continue to work with medical professionals for a lock tight diagnosis.