4 yr old with no fever and normal behavior but has some yellowish eye drainage and nasal congestion. antibiotics or let his immune system work?

Watch : I would monitor. Clean off the discharge with cool water vs. Warm. Warm water will increase redness and make it look like pink eye. If it persist more than 3-4 days then follow up with your pediatrician.

CONJUNCTIVITIS: Looks like bacterial infection to the eyes, needs antibiotics gtts. Or ointment.

Treat if red eyes: If he wakes up with eyes stuck together from dried secretions and a pinkish to red eye, i would treat. If no redness, not stuck together, and discharge is occasional and not heavy yellow or green, then can supplement with artificial tears 1-2 x a day or let it resolve in its own.