Very sorry to hear how Luch is feeling.
Vomiting causes can include:
- Dietary indiscretion (eating something you do not know about)
- Stomach or intestinal foreign body
- Something that was given to them (new food, new treat, human food)
- Intestinal parasitism (not just the worms, but the microscopic bugs like Giardia and Coccidia). They can cause vomiting also, not just diarrhea
- Toxin exposure would be less likely, unless you have reason to suspect exposure to a chemical.
At this age, there are very serious concern for foreign body ingestion, dietary indiscretion (ate something you don't know about), viral disease (yes, parvo, even if vaccinated).
For this age puppy, I would not delay. This is well worth a vet visit, to any vet, for supportive care.
To help settle the stomach you could give a 1/4 tablet of Pepcid A.C. 10mg antacid, or 1 tsp of pepto-bismol.
Do not try to offer any food right now. Vet visit first to get good supportive drugs.
I would expect the vet to consider doing a parvo test (even if no diarrhea), fecal test to check for other intestinal parasite issues, and start some good stomach medications.