May I know if gluthatione or metathione good or contraindicated to hypothyroidism? What is good medicine for patient with hypothyroidism?

I don't know what drugs your doctor would put you on but it is always good to follow a corrective diet to improve your health conditions

Nutrition and herbs can be useful as supporting therapies, but they cannot replace conventional treatment.
Nutrition and Supplements

* Avoid foods that interfere with thyroid function, including broccoli, cabbage, brussels sprouts, cauliflower, kale, spinach, turnips, soybeans, peanuts, linseed, pine nuts, millet, cassava, and mustard greens.
* Avoid refined foods, dairy products, wheat, caffeine, and alcohol.
* Essential fatty acids (1,000 - 1,500 mg three times per day) are necessary for hormone production.
* Vitamin C (1,000 mg per day), vitamin A (10,000 - 25,000 IU per day), B complex [(50 - 100 mg/day), augmented with vitamins B2 (riboflavin, 10 mg), B3 (niacin, 10 - 25 mg), and B6 (pyridoxine, 5 - 15 mg)], selenium (200 mcg per day), vitamin E (400 IU per day), and zinc (30 mg per day) can help promote normal thyroid hormone production. However, unless you are deficient in one or more of these supplements, there is no evidence that taking them will help hypothyroidism.
* L-tyrosine (500 mg two or three times a day) is a precursor to thyroid hormone and may help boost levels in the body. If you are taking prescription thyroid hormone medication, it is important not to take L-tyrosine without direction from your doctor. Do not take L-tyrosine if you have high blood pressure.
* Calcium (1,000 mg per day) and magnesium (200 - 600 mg per day) help many metabolic processes function normally.
* Do not take an iodine supplement unless directed by your doctor. Iodine is only effective in cases of iodine deficiency, which is uncommon in the developed world. And excessive iodine can cause hypothyroidism.
* If you take thyroid hormone medication, talk to your doctor before consuming soy products. There is some evidence soy may interfere with absorption of thyroid hormone.
* Iron may also interfere with the absorption of thyroid hormone medication.

Herbs

Herbs are generally a safe way to strengthen and tone the body's systems. As with any therapy, you should work with your health care provider to get your problem diagnosed before starting any treatment. You may use herbs as dried extracts (capsules, powders, teas), glycerites (glycerine extracts), or tinctures (alcohol extracts). Unless otherwise indicated, you should make teas with 1 tsp. herb per cup of hot water. Steep covered 5 - 10 minutes for leaf or flowers, and 10 - 20 minutes for roots. Drink 2 - 4 cups per day. You may use tinctures alone or in combination as noted.

Bladderwrack (Fucus vesiculosus) is often suggested as an herb to improve thyroid function, but that is because it contains iodine. Most cases of hypothyroidism in the developed world are not caused by iodine deficiency, and too much iodine can actually cause hypothyroidism. Avoid bladderwrack unless directed by your doctor.