There is a great natural supplement for the low thyroid called "Armor" it has no side effects and is not bad for you like synthroid can be at times. Have your doctor write you a prescription for it, you will probably feel better on it. Another good thing to take for the thyroid is Iodoral Iodine, however, it is a good idea to have the doc order the Iodine Loading Test for you and then test you for iodine levels. You can also add kelp, this is natural iodine and good for the thyroid, whether it be high or low. L-Tyrosine, an amino acid is good for thyroid support too.
Why are you are Zocor, this is for high cholesterol.
There are some discussions like this in Complimentary Medicine you might want to check out.