This all depends on what kind of thyroid problem you have of course. There are natural herbs that can be taken to help control the thyroid, such as Lemon Balm which is good for HYPERthyroid, and St. Johns Wort which is good for HYPOthyroidism.
I am currently out of the country so, getting my hands on the natural stuff is harder. I am right now taking 50 mcgs of levothyroxin a type of synthroid for my hypothyroidism.
There are a few new treatments that i have read about, but they are unsure if it will have an effect. They have T3 hormone in pill form, that you can take in conjuction with your T4 (synthroid). The idea behind that is that when they take your blood and measure how much T4 and T3 is in your blood, the T3 is usually inacurate simply because that hormone is found inside the cells of the blood and if your body isn't making enough it may not read that because there is still some in the blood stream. The T3 helps make the T4, so it really is a crucial piece in keeping you healthy.

But that treament may not be for you if you have hyperthyroidism which produces too much of one or both.
As an alternative prescription drug for hyperthyroidism, you have propylthiouracil (PTU)which is a hormone blocker.
An alternative for hypothyroidism would be Armour Thyroid and Bio-Thyroid which are both natural dessicated thyroid glands from pigs. (Ewww.. i know but at least its in a pill form.) Cytomel and Triostat are for hypo as well, and it says at drugs.com a little more about it being good if you are allergic to the other meds.
For more info on reputable sites on the thyroid check out wikipedia, endocrineweb.com, and thyroid.org for recently published thyroid research.

I agree that natural remedies can be great for some things, but not for the thyroid. Your body needs extreme regularity when it comes to thyroid hormones. Unfortunately, natural and animal-derived remedies tend to vary in potency.

Since you are on anti-thyroid medication, you obviously still have hyperthyroidism (so don't worry about all the thyroid drugs for hypothyroidism).

Have you asked if your racing heart could be caused by your thyroid imbalance?

When was the last time you had your TSH tested? It is possible you are on too much or too little of your anti-thyroid medication. If the anti-thyroid meds aren't working and the radioactive iodine didn't work (usually they try not to give you too much so you'll have some function left--I guess you didn't get enough), have you asked about having part of your thyroid surgically removed?

I do agree with the above poster about doing a ton of research into this topic. If the doctor doesn't like it, that's tough. He works for you! Never forget that! Personally, I'd get another doctor who doesn't mind answering questions. Make a list of all the questions you have and make sure the doctor answers them to your satisfaction. This is too important to let yourself be dismissed. We're talking about your health, your quality of life.

I know you've been to a ton of doctors, but once you find the right one, you'll be glad you kept fighting.

No disrespect, but Synthroid is not any more of a chemical than what your body makes normally. Just because it's natural doesn't mean it's not a chemical. Just because it's "natural" doesn't make it better for you or more like what your body produces.

To say that Synthroid and medications like it don't work is completely false. Millions of people take these medications to live normal lives with low thyroid production or no thyroid at all (such as myself). Perhaps some people have had problems getting the correct dosage, but that takes time and a doctor who bothers to listen when their patient doesn't feel right.

Perhaps Armour works for some people (I don't know one way or another), but synthetic thyroid hormones work as well. To discourage people and tell them that their life-preserving medication doesn't work is really irresponsible.