Eye inflammation with slight discharge

Blann's right eye had some discharge this morning. The outer eyelid is reddened, inner eyelids are only showing slight redness toward the corners of his eye. There is a little bit of swelling with the inflammation, but you have to be looking for it.
No scratches or abrasions on the eye.

He actually started to squint last night. Since he was asleep all afternoon and still was when I left the house at 3:30 I can't be certain that he didn't start squinting until we got home after 7 and started the fire - it was the fire that he stirred from the bedroom to go check out and then was sitting near when I noticed the squint around 8pm.

He has no URI symptoms, lungs are clear, no past URI infections during the months I've had him (from ~7wks old and on), and has never had his eyes bother him before. He is on a twice daily steriod inhaler for bronchitis that likely has an inhaled allergy trigger (anybodies guess as to what that allergen is…)
Does his eye irritation sound more allergy in nature to anyone else? I worry that the small amount of smoke from the fireplace will set that off and affect his bronchitis. Anyone with asthmatic cats and a fireplace? Or a cat with allergies that affected their eyes?

It might be because of the fire place. Or it could be a cold, the other symptoms may not be showing yet. Midnight's first symptom of his cold was watering eyes, then the sneezing came after. You should call your vet just incase.

He's already been to the vet. I don't make threads in place of veterinary treatment, but instead to get further ideas after I've already went.
His vet is the reason I know his eye itself isn't scratched and that his sinuses and lungs are clear.

Blann has some ointment for his eyes that we're to try for 5 days. Though the ointment seems to irritate his non affected eye a bit…

When I run the corn stove, sometimes it bothers Ophelia's eyes. She LOVES to sleep right in front of it, but I had to relocate her kitty bed so she sleeps somewhere near/warm but not directly in front of the air flow.

I don't know whether that's good or bad. Good because he wouldn't be sick, but bad because if it can bother his eyes its only a matter of time till it bothers his bronchi.