Well, that, I will tell you is a very involved concept, but I will condense it here and give you what you were asking for: iodine sources. However, keep in mind that the thyroid is a complex gland and has a LOT of other things behind it.
How do you know if you need iodine? I do an iodine chart with my clients to help them assess this. Your medical doctor may have already confirmed this.
Because you are concerned it is a thyroid problem, and I am a holistic practitioner, I would ask you to look into your life and your self and see what could be behind the fact that your problem developed in your thyroid. What are you holding yourself back from? Are you speaking and living your truth? Are you speaking up for yourself? Being creative? Feeling like you are a valuable person? Or maybe there is something you need to speak out about that you are not. Where is there imbalance in your life? Since the thyroid is a 2 part gland, one side could be compensating for the other. Where are you doing this in life?
While there are many layers in a life that need to be examined to have true health, the sources of iodine that are MY favorite include:
A supplemental seasoning called "Gomasio". It is dried and powdered sea vegetables which are FANTASTIC for nourishing the thyroid.
Also, hope you love sushi, because the seaweed and other sea vegetables are fantastic.
Things like Nori, dulse, kelp, are the best sources and serve the body in many other ways too. These are typically found in asian and viet tien markets, but if your stomach churns at the idea, then go with Gomasio. It tastes like and replaces salt at your table.
I don't love the idea of iodine supplementation unless your doctor has prescribed it, as it is definitely something that has to be monitored.
For other in depth help with your functional wellness, schedule an appointment. Each body is different and your cells or coded differently than the next. There is no ONE STOP SHOP when it comes to the cureall for thyroid.