Is it possible to have an allergic reaction to Methimazole like swollen and puffy eyes? I was recently diagnosed with Grave's Disease. I started taking Methimazole on a Wednesday and on Saturday my eyelids were swollen and I had puffiness under my eyes as well. I stopped taking the medication and the swelling and puffiness seem to be going away. My doctor said she does not believe it is caused by the medicine.