Hello:
Congrats on the new puppy :) He may have allergies or an upper respiratory infection. You can flush the eye using sterile saline solution twice per day and use it to wipe the eye as needed. Do see your vet with him as soon as you are able as he will likely need antibiotics to treat it. Also, make sure you deter him from pawing or rubbing the eye. Use positive redirection like a safe chew treat like a bully stick or stuffed kong toy, to keep his mind active and off the eye. Good luck and hope he feels better soon. :)
animal care specialist
15+ yrs pet health care, breeder of English Mastiffs, barnyard, knowledgable aquarium keeper