Ah yeah most doctors would see less than 4 TSH levels as acceptable, but you can ask for a more in-depth test to check your T3 and T4 levels, for a more accurate look at what's going on.
When mine was 17 I was barely getting out of bed, I was that unwell with it, and they put me on 25mcg thyroxine, increasing every three months by 25mcg. By the time I got to 8 I was feeling better but still unable to lose weight - it wasn't until I got down to 3 that I was able to diet and see results! I had it checked when I was 4-5 weeks and it was about 2, which is amazing, but haven't had the results of my last test.
Good luck at the doctors. If you believe there's something going on, push for that other test. There's also a horrible test they do where they take a biopsy from your thyroid through your neck, which I managed to avoid. My mum had it done because her levels were fine, but she still felt she had a problem. I hope you avoid that!!!