Your chicks may be dealing with respiratory disease such as MG (if they weren't pecked around the eyes.) MG can show up in young chicks after about 3-4 weeks old, and may be from the hatching egg or from a carrier chicken that they were exposed to. I would read this link about respiratory...
I have no idea why your vet told you this. The only difference in the 2 ointments is Neosporin has neomycin in it. Both Polysporin and Neosprin have bacitracin and polymixinB in them. They prescribe it for people every day, and BYCers use it all of the time in their chicken's eyes. There may...
I would clean his eyes with a warm wet compresses while you are holding him. This will hopefully get the dried blood off. Then put Neosporin ointment inhis eyes once or twice daily. His eyes may be okay after the swelling goes down. Many of us have sworn that a chicken has lost an eye only to...