Hello
Will advice you to consult your Doctor but om a regular basis we suggest to go for following test-
TSH, T3 and T4.
One can start paleo Diet but better to do under supervision. This diet usually omits processed food, cereals, dairy, starches and incorporates more of fruits & veggies, lean proteins like fish chicken , nuts etc. Since you are having hypothyroid better to avoid Brocolli, Cabbage, cauliflower, mustard, Turnip, pears, strawberries, peanuts, soya.
Wish you good luck. Do check my FB page www.facebook.com/eatomatic for more health tips.