Might consider stopping the neomycin as 10
% of people taking it develop allergies to it.
Might consider just using the dexamathason for a 7-10 days.
I'm assuming you do not wear contacts. If you do the contacts are the cause 99% of the time.
There are many things that you could be allergic to that could cause this including cosmetics, hair coloring, nail polish, food allergies, perfumes, etc.
If you get no relief consider seeing a cornea/external disease ophthalmologist.