There are actually 3 surgeries that are performed - orbital decompression, strabismus surgery to correct double vision if necessary, and eye lid retraction surgery. You could need only 1 or all 3. However, the surgeon isn't likely to do anything until you are followed for a while and they make sure your eye disease has "burned out" - that is, stabilized. I didn't have any problems with my vision, but the symptoms (bulging eyes, dry eyes, tearing, decreased mobility) warranted the decompression and the eyelid surgery. It has been a year since my second surgery and I am so happy to have that chapter of my life behind me.
Find a good Ophthalmologist - preferably one who treats Thyroid Eye Disease regularly. Mine was an Orbital Reconstruction specialist. The early you get treatment, the easier it will be for them to keep track of the changes in your eyes.
The only thing I have to add to the above list of things to try is a night lubricating gel (like Refresh PM or something similar). It helped quite a bit to keep my eyes from drying out at night when my eyelids didn't close all the way.
Good luck to you.
Most doctors won't do surgery unless your vision is compromised and ask you to wait it out. Try elevating your head when you sleep, stay hydrated, use eyedrops and take flaxseed oil. All these things help....the first step is to try and get euthyroid as soon as possible.