Some snorting or sniffling noises are normal.
If your pup gets more stopped up (congested) sounding after being outside, it could possibly have allergies.
The usual signs of a sick puppy are:
1. Uncurled tail
2. Discharge form the nose or mouth
3. Abnormal temperature, normal for a pup is around 101 F.
Also look for redness in the ears.
Vomiting alone is not a sign your pup is sick, but should be considered as a possibility. Grass does not make puppies throw up, it helps them to throw up, dogs usually eat grass when they have an upset stomach.