There is nothing holistic to treat hypothyroidism. You are hypo, because for some reason, your thyroid is not producing enough hormones. The only way you can treat that is to replace the hormones.
As gimel said, sometimes this can be done using a T4 medication, such as synthroid, generic levo, Tirosint. The active ingredient in each of these is identical to what your body produces, but both synthroid and generic levo have fillers/binders that can cause adverse reactions. Tirosint is a gel cap, whose only ingredients are the levothyroxine, water and glycerin. It's about as hypoallergenic as it gets.
Cytomel is a T3 med that is often added with the T4 med, if the patient does not, adequately, convert the T4 to T3.
Armour and Nature-throid are T4/T3 combos. These are made from pig thyroid and contain both T4 and T3.
Any of these can work well, but because we are all so very different, it sometimes takes a while to figure out the med/dosage that will work best for you.
There are a number of conditions that lead to hypothyroidism. One is Hashimoto's Thyroiditis, which results from the autoimmune system incorrectly identifying the thyroid gland as foreign to the body and producing antibodies that attack the gland until, over an extended period, the gland is destroyed. The cause has yet to be determined and confirmed with scientific studies.
Another condition is secondary hypothyroidism, in which the pituitary does not produce enough TSH to adequately stimulate the thyroid gland. A third condition is called silent thyroiditis, or subacute lymphocytic thyroiditis. The latter condition is described in this link.
http://www.ncbi.nlm.nih.gov/pubmedhealth/PMH0001425/
Of the three, the first two are not reversible, but they are treatable. Silent thyroiditis is also treatable, and as you will read in the link, it does go away in about a year.
The symptoms you mention can be associated with being hypo. Even though you are taking medication, it may not be enough, or it may be the wrong kind. T4 meds can work well, if you take an adequate dose and your body converts the T4 to T3 adequately. If not, then switching to a med containing T3 becomes necessary. Those are the situations where a med like Armour Thyroid, or Nature-Throid, or Cytomel are used.
If you will please post your thyroid tests and their reference ranges shown on the lab report, members will be better able to assess the status of your testing and treatment.