Worried about my cats eye

So I've had this kitty for 3 weeks now. I took him to the vet the first week I had him and was disease tested and updated on shots and worming.

Well lately I have noticed the rim around just one eye is looking red. He isn't squinting, no discharge or watering, no swelling and I can't see the third eyelid. He's also not sneezing or coughing. He does have a bit of reddish brown crust in the corner, but it's just a tiny bit. He doesn't rub it or seem to be bothered by it, his only symptom is literally the redness around the rim.

I'm going to call my vet in the a.m, but in the meantime I'm worried he's contagious or something and he's been in close contact with my other cat. I took a picture, which isn't the best, but it's his left eye. Any thoughts of what it may be?

It might be some mucus that accumulated in response to an irritant, such as dust or even printer ink dust, etc.  Since he isn't displaying other signs of illness, that would be my first thought. You could gently swab his eye with eye wash for human if you have some on hand - if his eye is irritated, it might sting a little so you might dilute it with some warm water and then dab on a tiny bit of vaseline or coconut oil  as a soothing ointment. If he is resistant to the washing, you can skip that step & just apply the ointment. IF the redness continues, your vet may have you use an eye ointment - I prefer anything that doesn't have sulfas cuz that can sting more than gentamycin or polysporin eye drops. By the way, what a HANDSOME boy!!!

Thank you catsknowme , I'm scaring myself silly ready about conjunctivitis online! I'm thinking my other cat may have caught the corner of his eye during one of their very rough play sessions, or I might not have rinsed lotion off my hand well enough before petting him and he rubed some in there. He loves to ram his face into my hands and just rub all the way up my arm. I say ram because that's literally what the does! He's very resistant to me handling his face or him for that matter. He wants attention but as soon as he senses me trying to look at something he starts to fight me. And thank you, I think he's quite adorable too