I totally agree with everything Paxiled said.
The first thing we need to know is whether or not you are taking replacement thyroid hormones to get/keep your thyroid levels under control. As Paxiled noted, adequate thyroid medication will go a long way toward helping get things back on the right track.
Hashimoto's is the most common cause of hypothyroidism in the developed world, so if you haven't determined the cause of your thyroid condition, this would be a good time to do that. That's done by testing for thyroid antibodies, Thyroid Peroxidase Antibodies (TPOab) and Thyroglobulin Antibodies (TgAb). If either/both are elevated the diagnosis would be Hashimoto's.
You should also be tested on a regular basis for Free T4 and Free T3 - those are the actual thyroid hormones and many doctors don't regularly test those. Many only test TSH, which is actually a pituitary hormone and does not always, even often, correlate with thyroid hormones, especially when one is on a replacement thyroid medication.
Even if you're tested for Free T4 and Free T3, just being "in range" isn't good enough... We all have our specific point(s) that we need to be and if our medication dosages aren't adequate, we won't achieve optimal levels.
All of that said, there may be other things involved as well since many of us with Hashimoto's/hypothyroidism also have various vitamin/mineral deficiencies and/or other conditions that also affect our metabolism.
Iron, vitamin B-12, vitamin D are all necessary for proper metabolism of thyroid hormones and many of us are deficient in the nutrients, plus many of us have malabsorption problems as well. Adequate testing is necessary to determine what, if any, further issues you might have.
As far as diet, I can't say much more than Paxiled already said. I don't know of anyone who doesn't eat at least "some" vegetables. My husband is one who eats the least of anyone I've ever known and even he eats a salad now and then that includes lettuce (even though it's iceberg which little/no nutritional value) and tomatoes. He eats corn and potatoes, both starchy, but they are veggies. He also eats sweet potatoes (though they have to candied) and on the rare occasion, he'll eat a helping of cole slaw or baked beans.
I was never really big on veggies because there were a lot of things we didn't have when I was growing up, but I've gradually learned to eat a pretty large variety of things. You can change the way things taste by adding herbs, spices, etc or cooking them in different ways. That's what I've done to make my diet more healthful and to add more veggies.
Try walking through the produce section of your local grocery store and pick out a couple of things to try, then go home and find recipes for them. One thing I've learned to make is "zoodles"... what's that? Zucchini noodles. I bought a $10 spiralizer and instead of making spaghetti to eat with my sauce, I make my noodles out of Zucchini... I have almost no calories involved in the zoodles and with the sauce, I can't even tell I'm eating Zucchini instead of pasta. You can eat spaghetti squash or yellow squash the same way. You can hollow out cucumbers to make a "boat" for tuna or chicken salad or make a sandwich with sturdy lettuce leaves instead of using bread... there are all kinds of ways you can incorporate veggies and barely know you're eating them. Eventually, you'll even start to like them...
My husband and Paxiled's brother could almost be the same person or at least closely related... except my husband does not eat a disciplined diet as far as the sugar is concerned. In fact, he eats tons of it, drinks soda, etc. He does not have a thyroid condition and he's quite slender, but he's also not healthy, though he doesnt believe that. He thinks if one is thin they are healthy, but he doesn't see that layer of fat under his skin, either. He's lost muscle strength, has some memory issues, has had bladder cancer (disputed), colon resection, etc.
All of this said, you'll find a lot more information about hypothyroidism in the Thyroid Disorders forum. Please feel free to acces the forum via the following link: