First of all, I just wanted to say that I'm so sorry that you are facing thyroid cancer. I went through the same thing 11 years ago now, and it really is a life-changing event. But the good news is that it IS a curable form of cancer, and you can and will have a normal and healthy life in its wake. I felt depressed for quite awhile after my surgery (also a complete thyroidectomy), partly due to not having an adequate dose of thyroid hormone yet, and partly due to the diagnosis at the age of 31. But 11 healthy (just a little too fat! lol) years later, and 3 beautiful babies later... I can tell you truthfully that it hasn't held me back at all and I rarely even think about it anymore. I wish the same for you. ((hugs))
Now as for the diet, when I was diagnosed and went through my treatment, it was the one time in my life that I was on Atkins. I had lost about 25 pounds on it, and while finding that I was constantly craving sweets breads and fruit, I felt otherwise well. The best part was that although I was low thyroid for quite awhile after surgery (to get through the testing phase when you have to have no thyroid hormone in your system), I didn't gain weight on low-carb. And that's almost unheard of for someone who's REALLY low on thyroid hormone for weeks. So it definitely works. But I couldn't do it forever - it was just too restrictive for me. I went off it after 2 years, and gained all my weight back over the next 2 years or so.
So now I'm doing calorie counting, which for me, is far less restrictive and matches my lifestyle better. Not low fat, just calories in, energy out... I aim for 1400 a day and try to exercise 1/2 hour a day. It's been working (my ticker doesn't show that I was up to 274 at my highest 3 weeks ago and have since lost 11 pounds... too depressing to change it at the time lol). So it does work too. You just have to figure out which method will enable you to keep it going consistently long term.
All the best on your journey... I wish you peace, strength and health.
