Right off the bat I wanna state we’ve already been to the vet!

A few days ago I noticed my cat had watery eyes and his third eyelid was showing a little bit. We took him to the vet and she said his eyeballs look fine but that the third eyelid showing is a sign of some sort of stomach/intestinal problem. The vet gave him a dewormer in case he had some worms we didn’t see and told us to monitor him. She said he seemed completely healthy and I haven’t noticed any behavior changes so I can’t imagine there’s anything wrong but we’ve used the the dewormer for about a day and his eyes haven’t cleared up, she told us the next step if he doesn’t get better is bloodwork. I’ve never had another cat experience this so I’m not sure how worried I should be. I don’t have a picture of his eyes at the moment but I’ll try to find one.