Our George gets eye infections all the time. The vets says gentically his eyes are too narrow and his tear ducts are blocked. Poor baby boy !! (Might be why he was abandoned orginally ?)

As a preventive measure, we wipe the corners of this eye twice daily with eye wipes. We must keep the company afloat, with our purchases.
When he gets an infection we get a cream to use twice daily in his eyes, from the vets.

I think the eye wipes are a good thing to use generally but it sounds like your kitten may need some additional treatment.

I am pleased that you are going to the experts tomorrow, let us know that the vets say tomorrow.