Hashimoto's thyroid condition under control but always sick!!?

I was diagnosed a year ago with hypothyroid condition called Hashimoto’s, I take my thryroid medication everyday, and have my blood levels checked every 3 months. The Doc says my hormone levels are good now. However, ever since I was diagnosed with this, I catch every bug around. As soon as I get over a bad cold, a few days later I have an ear infection, then a couple of weeks later bronchitis, then a stomach flu and so on… I eat healthy and keep active (when I am not sick in bed). I keep good hygene and live in a healthy environment ( near the Alps!) but keep getting sick. Anyone out there with a similar problem? Is there anything I can do to strengthen my immune system or are people with this thyroid problem doomed to a crappy immune system? I am so embarrassed to always be sick.