How can I comfort a 5 mo. Old with allergies? Red/goopy eyes. Bad runny/stuffy nose. He wakes up with his eyes gooped shut:- (

Pink eye. Babies do not have sinuses that are fully formed so when they get congested it will often back up to their ears or run out their eyes. If your baby is fussy and his eyes are draining and red he needs to see his pediatrician. He is unable to communicate other than to let you know he feels bad. His pediatrician will help with the rest.
Allergies? This may not be allergies. Is he febrile? Is this a new onset? He may have a viral issue, and conjunctivitis. I would see his pediatrician asap. Stuffy noses in infants are treated with saline and syringe/ bulb.