I noticed something there is a white thing in my tortoise's eye couple days ago. I tried soaking it in water and rinse its eye hoping it will come off, but it seems stuck no matter how many times I try to flush it off.
That may be the third eyelid, however it's hard to tell from the picture. Normally when the third eyelid swells, it comes from the corner of the eye, not the top as it looks to appear in the picture. Only thing I can think of to offer you is to buy some eye ointment and treat the eye a few times a day until the swelling goes down.
First flush the eye with sterile saline (You can buy this at the pharmacy in the contact lens department), then apply the ointment. You can buy it online: