I too have  hypothyroidism.  Like you my doctor put me on a diabetic diet.  I'm not diabetic.  It is the best diet to lose weight and stay healthy doing it.  However, it does take a long time for it to be effective due to the thyroid disease.  In 6 months I lost 20 #.  At that rate it would have been 80# in 2 years.  Now that is a significant amount of weight.  But, I gave up after just 6 months.  There is no magic bullet.  It takes lots of determination and even more effort but, it can eventually be done.  If your serious, stick with it and don't quit. [God doesn't like ugly and quitters even less.]  Good luck!