I just did a quick search and found an article that contained a list of herbs one should avoid with hypothyroidism:
Astragalus - can contain potentially toxic levels of selenium and can interfere with medications that suppress the immune system, blood sugar and blood pressure--which may be fatal.
Bladderwrack - Prolonged use of bladderwrack has been shown to cause goiter and increase the risk of getting thyroid cancer. Bladderwrack, being a seaweed, is also prone to high levels of toxins such as heavy metals like arsenic found in ocean water.
Echinacea - many thyroid conditions and cancers can worsen with the use of antioxidants
Garlic - one of the adverse reactions of garlic intake is the onset of hypothyroidism. (my note: this refers to taking garlic as a daily supplement; it doesn't mean you can't use garlic as an ingredient in cooking occasionally).
You should also be very careful taking supplements that contain iodine, such as Kelp or other seaweed products, if you have Hashimoto's as iodine can make autoimmune attacks greater.
Herbs used to help with hyperthyroid symptoms include:
Herbs to help with hypothyroid symptoms include:
Herb used for both hyperthyroidism and hypothyroidism: