Welcome to the forum. You might try going to the following link and watching some of the testimonials for encouragement:
If you are struggling with RT3 issues, have your doctor perform a Spectracell test. (www.spectracell.com) Selenium deficiency is often linked to this problem. You will also want him/her to perform an iodine loading test. Iodine deficiency can also be a nutritional problem with thyroid disease.
You are not regular because your thyroid is not functioning properly. The following link on thyroid and nutrition might be beneficial to you:
Constipation is a common symptom of low thyroid. I would focus on continued liberal consumption of vegetables in your diet. As far as a list of what you can eat, try the recipe section of the forum. There are more than 300 species of vegetables, fruits, and nuts. Video #13 under the Glutenology tab lists all of them.
Thanks for your question!