I am sorry to say that PCOD and HYPO thyroid problems cannot be cured but yes there is a silver lining as they can be treated to some extent.
Treatment of thyroid related problems:-
1) Daily intake of thyroxine tablets can help in replacing the already missing thyroid hormone in body. This will treat hypothyroidism but however symptoms persists or diminishes gradually on their own.
2) Inhibiting activity of thyroid peroxidase which in turn will help thyroid to become inflamed and this can be done by eating large amounts of soy. Thus you need to check on your soy intake and if possible try to eliminate it from your diet or decrease its quantity greatly as it is not good for thyroid disorder.
3) Avoid sugar intake greatly as hypothyroidism worsens insulin resistance in body.
4) To produce thyroid hormone in body, iodine plays a very important role and thus you should concentrate on your daily intake of iodine and include dairy, iodine rich salt, chicken, fish, green leafy vegetables and all those products which are rich in iodine.
5) Try to have a gluten-free diet.
6) Eat a healthy well balanced nutritious diet which includes lots of fruits, vegetables, sprouts, dairy etc.....
You are not losing weight in-spite of taking thyroxine and estrogen tablets because your condition makes difficult for your body to make use of insulin. Insulin is essential for body as it metabolizes foods into energy. Insulin resistance that is created in body will lead to build up of sugar and insulin in blood. Increased level of insulin results in production of male hormone androgen which is responsible for your acne, growing of body hair, irregularities in menstrual cycle, weight gain etc..... Though you are taking medication you cannot expect overnight results. These medications have to be taken for life time and you have to struggle with your weight issue. However, if you struggle a little more and make right choices and change a little pattern in your life style then may be you will start losing a little but gradual and consistent weight loss is for sure. Long term approach in your dietary pattern can help you greatly.
Here are certain tips that will help you in weight loss:-
1) Always prefer foods that will lead to low glycaemic load on body. These kinds of foods will fight with both insulin resistance in body as well as PCOD. Consume foods which are close to nature.
2) Good lean proteins are very essential for you. Include nuts, dairy, eggs, broccoli, cauliflower etc.....
3) Include good fats in diet like Omega 3 and Omega 6 fatty acids. You will not able to lose weight without including good fats in your daily diet intake.
4) Avoid or greatly decrease bad fats in diet.
5) Eat lots of nuts which are popularly known as super foods. Eat right amount of walnuts and almonds daily as they are rich sources of Omega 3 fatty acids, Vitamins B and E, and minerals like potassium, calcium, manganese etc.....
6) Include all sorts of fresh fruits and vegetables if possible organic would be more beneficial.
7) Avoid fruit juices.
8) Avoid processed foods.
9) Avoid refined flour, rice and sugar.
10) Exercise daily. Weight training and resistance training a little daily will increase your metabolism making your body to burn those stored calories in the form of fat.
11) Daily half an hour walk is very beneficial.
You mentioned that you are in depression. This is common because all the hormonal changes brings stress but you need to learn to relax. Stress will further affect your body and you will struggle more with your weight loss problem. You need to accept with what you are dealing with and try to instill a lot of positive attitude in yourself. This will motivate you to come out of your situation and decrease your body weight. Also sleep well. Getting enough 8 hours sleep is essential for weight loss.