My cat has constant clear eye discharge that I can’t wipe away and sometimes glues the eye shut

From the photo, the cat shows conjunctivitis. Causes include bacterial infection, herpesvirus, chlamydia, or mycoplasma. Bacterial conjunctivitis is usually treated with anti-inflammatory eye drops and oral antibiotics, with an Elizabethan collar and good ventilation, and the cat generally recovers in about a week.

If feline herpesvirus (cat flu) causes the conjunctivitis, the treatment period is longer and usually requires antivirals, interferon, immunity boosters, and antibiotics, possibly 2-3 weeks to recover or even lifelong carriage with recurrence. If symptomatic treatment brings no relief, go to the hospital for respiratory pathogen screening to confirm the cause and an effective plan.