What are my treatment options for puffiness/fat bags/circles under eyes from thyroid eye disease? (Photo)

If you live in a major American city, likely in your community there is a University based Oculofacial surgeon who provides the bulk of this care. In the largest cities there are specialist in private practice who also offer these services. There is a new drug approved to control active thyroid eye disease. Only a persona consultation will determine if you are a candidate for this. It can reduce the prominence of your eyes. The treatment is very expensive with significant side effects and it is not for everyone. The first step is to determine if your thyroid eye disease is stable.  Once you are stable, decision have to be made regard on what type of surgical rehabilitation may be needed. The new treatment (teprotumumab) if you are a candidate can reduce the amount of eventual surgery you might need. As a temporary measures, yes filler can be helpful. 

You have in the postinflammatory stage of Graves eye disease before doing eyelid sugery. You will likely benefit from blepharoplasty at that time. It is important to preserve eyelid function so technique is critical. See an expert.

Once you condition is stable and under full control, you may consider consultation with a board certified plastic or occuloplastic surgeon (both with experience with few patients with this condition) regarding transconjuctival lower blepharoplasty. This provedure will correct bags and groove underneath. Good luck.