I'm sorry to hear about your cat‘s eyes. If attempting to treat at home you want to be very careful first of all that the eyes continually looks better through treatment, and no signs of rubbing at it, reddening worse, or cloudiness appear in the eyes. This can be conjunctivitis or an allergic reaction.
You should rinse the eyes with sterile saline, like that found in regular contact lens solution, (not the ones with disinfectant but just normal saline/ NaCl) and do not let the tip of the container touch the eyes. You can wipe around the eyes with the saline soaked on a soft cotton ball or gauze, but don't use anything harsh like paper towels.
You can also find an ophthalmic antibiotic ointment at a pharmacy: like terramycin, triple antibiotic (neo/poly/bac), etc. Ask the sales people if you need help, but it does need to be safe for the eyes, not a topical one for skin. After rinsing the eyes, apply the ointment 3 times a day (every 8 hrs) for 10 to 14 days to each, even if looking better well before then.
There could also be a scratch or ulcer forming if your cat rubs at them and if not starting to clear up in a couple of days, you'll need a vet to check it. It is very possible some debris or litter settled in your cat's eyes, causing this problem.
Best of luck, and let me know if I can help further.