You must have developed allergic reaction
. Try blinking your eyes a couple of times in a handful of water, a dose of cetirizine
compresses with anti allergic topical eye drops will help you until you are examined by an ophthalmologist for any remains of the cats hair follicle or any dust inside your eyes.
If you have pain and redness
with discharge it may be an infection too
You have not mentioned the name of the antibiotic! and it is not advisable to use others eye drops.
A single dose of antibiotic will not help you reduce the swelling immediately until the reason for the swelling is eliminated.
I would suggest a consultation at the earliest. Take care.