Kitten Keeping Eye Closed

My 6 month old kitten has been keeping one of his eyes shut all day. I put some contact solution in it to try to wash out anything, he seems to be opening it a little bit more, but still keeping it shut mostly. The lids look pink and irritated, when I open his eye the whites, pupid, iris, look fine, not cloudy or discolored. It just looks irritated and watery. Anything I should be concerned about, or look out for, I don't want to rush to the vet until I know for sure it's not just like some litter dust in his eye or something.

It's possible he has an abrasion on his cornea. My cat had one and it presented similarly to what you are describing.
He needs to see a vet. They will apply a "stain" to his eye to see if there is an abrasion. If there is, treatment (depending on the size of the abrasion) typically is eye drops and pain medication as this is a painful condition for your cat:

http://www.vcahospitals.com/main/pe...ticle/animal-health/corneal-ulcers-in-cats/77