They do look a little sore bless him!!

From what i can see the inner eyelid the, white bit that is showing in the corner doesn't look too red. If this does go red or even pink all over then could be conjunctivitus which clears up on it's own anyway.

My cat has been having a few weepy days the past few weeks, am guessing it's allergies, i'd only be worried to take him to the vets if the gunk is green or yellow, just like humans it's a sign of infection, but if the weeping is clear i'd give him another day or two and see if he gets better, just keep bathing them like Alexandriauk says with tea, i just usually use a teabag, wait for it to be a little bit warm and wipe his eyes with it, if you can get a bit of warm water, and try to rinse his eye out. Be very careful though for it not to be too hot. I find cold water shocks the little mites and it's no fun getting them to co-operate after a shock!!

Hope he's feeling better soon!!

And like sadnomore says he should be due his first vaccinations so you could just get them booked and have his eyes checked while you're at it!! (Sorry didn't see your other post!)
The third eyelid is just another bit of protection for the cats eye, this closes over the eye from near their nose as you can see on your little monster!! You usually can't see them as much, and them being seen is a sign of an irritant in the eye!