You had a doc tell you that you can't have Hashi's because you are hypo, not hyper. Find another doc; she's seriously misinformed. Have you been tested for any of the several antibodies that are associated with autoimmune related thyroid conditions? That's the primary way one tests for Hashi's.

Regardless, 2.88 TSH is still on the high range of normal. Are you still experiencing hypo symptoms? If so, then lobby for an increase in your Synthroid. But, seriously, I have grave doubts about this doc.