Yes, please use eye drops through out the day, but also use the night time eye oniment, that can even be used during the day as well.
I suffer from TED, due to having graves (had a TT 16yrs ago). I have been under the care of a neuro opthomologist. Infact, I go back this week to see if it is time to discuss "surgery". I am having a lot of pain due to pressue in the eye sockets. My eyes do bulge out, but they could had been worse, but bulge out none the less..
Graves affects in 2 way,,usuallt the thyroid or the eyes (TED- thyroid eye disease).
I feel it has affected you with yr eyes.
There is a member here who unfortunately hasnt been online as she is caring for her husband after surgery but she would be brilliant to advise you.
Take a look at her profile , her journals and her pictures.
Her name is Marpo1.
This lady is an inspiration to all who have or is suffering from TED.
You do need to see an OPTHAMOLOGIST (not an Optometrist) for an evaluation and most probably eye drops will be given to decrease the pressure at the back of the eye as this is what causes the eye to come forward.
Marpo went through years of BOTH eyes being affected and now her eyes are NORMAL after many decompressions and surgery.
As I said...this lady is an Inspiration to ALL.
Personally I dont think a thyroidectomy would take away the eye problem but this should be discussed with the Endo.
Good luck and let us know how you go.