20032003 I have suffered with eye problems on and off for years because I have dust/mite/mould/cat allergies.
Periodically I get what you are describing though funnily enough not so much recently. I always thought of it as an infection rather than an allergy because it would be very bright red from tear duct to centre and sometimnes over the other side and only on one eye. It often used to occur when I had an important meeting or eg if I had to do some training ( this was when I walked in Local Authority) or something where people would be looking at me so very embarrassing. I never got the sticky pus with it, but it did itch slightly. It always used to go when I used Brolene antibiotic Eye drops and I was buying these constantly. I don't know why I rarely get it now?
Like babyjane I also have chronic but mild blepharitis (on my lower lid) but that is completely different and in mild cases does not cause reddening of the conjunctiva - but some itching of the actual eyelid edge and on close inspection slightly raised bumps. You can barely see mine and doesn't have pus either!
You should not share eye drops - in case of possible cross infection. Get your own drops! Not sure why yours recur so frequently - have you seen the doctor? Anyway try Brolene Eye Drops when it next happens and see if it does the trick.
Hurdity x