Hypothyroidism refers to inadequate thyroid hormone production. Thyroid hormone is very important for human body to keep warmth and maintain functions of each organ. With no enough thyroid hormone production, people will feel sensitive to cold, difficult in keeping warmth, fatigue and depression. It would cause very dry skin and fluid retention under skin for bad circulation, so it is possible for you to have puffy eyes from hypothyroidism. Meanwhile hypothyroidism might cause protruding eyeballs, which might make your eyes enlarged and puffier in the look. You should go to hospital for medication. Intake some iodine supplement which can help control the symptoms. Apply some warm compress and tender massage to help alleviate the retention of fluid around eyes. Ptosis might be caused by hypothyroidism for its impact on nervous system which controls the position of eyelids. It is better to get treatment earlier. Good luck to you.