First, TSH means nothing. Run as fast as you can from any doctor/endo that doesn't understand this.
Second, you will need weeks and weeks of combined fasting to correct your condition.
Third, you may have to throttle back your thyroid meds while fasting. This gets tricky because the half life of the synthetic T4 your are taking is about 2 weeks. So you may get away with a week long fast and then after the fast you may go hyper until your body readjusts.
It is likely that your hypo is being caused by halide poisoning, specifically Bromide. You need to detox this poison as well as the other halides such as fluoride and chloride. Check out this guys Iodine book and Thyroid book, they're a must read: