Hi, A.,
Pink eye, like any infection, will go away in it's due course. Though you don't need the antibiotic to solve the problem, it does make it go away faster. The problem you must watch for is reinfection, spreading it to the other eye, potential injury to the eye, or spreading it to the rest of the family. This can all be prevented with proper hygiene practices.
So, start off by making sure that everything is kept very clean. This includes everything your son and husband touches or puts their face onto. Do not let him touch his face and be sure that everyone washes their hands often. Break out the Lysol spray...this stuff is HIGHLY contagious.
For relief from the itching, swelling, and pussy eye, put a wrung-out hot wash cloth on his eye. Get all of the yucky stuff out of the edges where the tear ducts are and try to keep it as clean as possible. It may also help the itch to buy a bottle of saline solution (found in the contact lens section of the pharmacy, but ONLY get saline...no "multipurpose solutions") and use it to flush out the eye. Put the bottle into some warm water to bring it to body temperature so it isn't a shock for him when you put it into his eye. Also, if you aren't able to get the pus out of the very corner of the eye, try swiping the inner lid and corner with a Q-Tip wetted with saline solution. That usually does the trick.
It is likely that he will wake up in the morning with his eye encrusted with dried pus...DO NOT let him rub it off or pick it off as this can damage his eye if bits of dried pus get inside...again, use that nice warm, wet wash cloth to soak the stuff off and gently wipe away, then flush with the saline to get any smaller bits out. If his eye ends up being scratched while it is already infected, you risk a secondary infection of the iris, which can cause permanent damage to the cornea.
Hopefully this will clear up quickly and easily...I've found that if I use the hot wash cloths several times a day for about 3 days the infection usually clears up on its own with no medical intervention.
Hope this helps!!!