Chronic Runny Nose in 3-Year Old?

Could just be an allergy. Some of them are pretty bad this year. My son started showing signs of allergies around age 4. He would sneeze about 40 times a day, in groups of 4 or more. Started when he began K4... I think they probably had some mold in the a/c units or something that triggered it for him. He is allergic to molds (and other environmental stuff, like oak pollen, rye grass, etc). His allergies worsened as he got older. Now he is getting allergy shots to help reduce his symptoms and he is getting better.
Down to a set of shots every other week, and a Zyrtec every other day.

I used a q-tip with Vaseline on the end of it and lubricated the inside walls of my nose.

Likely allergies or possibly a sinus infection. My oldest has spring and fall allergies, and his nose runs chronically. It's usually VERY clear though. My youngest has gotten a sinus infection the last two winters in a row, which lasted 2-4 months - kinda waxed and waned during that time though. Some antibiotics finally cleared it up. It was not quite as clear as the allergy thing though.

its probably allergies. try nasal rinses to flush their sinus' (it takes a while to get used to because you feel like your drowning). or just give a 1/2 tspn of benadryl