Thyroid issues and the Air Force?

Last June I was diagnosed with hyperthyroidism. A few weeks later I had my thyroid killed off with radioactive iodine. Its been a year and I have been taking my medicine to control my hormone levels everyday and things have been going well. Technically, since I don't have a working thyroid, they say that it would be like having hypothyroidism. I am wanting to join the Air Force soon and I was curious as to if I have to take my medicine everyday for that if it would disqualify me to join. I heard from many that as long as it is controlled that it shouldn't be an issue. Though, I would like for someone who knows what they are talking about answer my question, rather than guess what they think. Thank you.