Of course with any young pup my initial concern would be a possible foreign body ingestion like a toy, string, shoe laces, etc. This is especially important if he is a chewer in the first place. There are several other causes to vomiting which include a virus, dietary indiscretion (eating table scraps), or even intestinal parasites. Monitor his bowel movements. Make sure he is going and it is solid. A change in diet could also cause vomiting though diarrhea is normally the result of a diet change. I would withhold any food tonight and only allow him small amounts of water. Try to feed him just boiled chicken and rice in the morning (a very small amount). If he is able to keep this down then you can offer him some more. If he does vomit, it is time for a veterinary visit to rule out other causes including those mentioned above.
Thank you
Theresa
Having bowel movements tells me that right now there is not an obstruction, that doesn't mean he hasn't eaten anything he shouldn't just right now it is okay to wait a little while longer before panicking. If you can, run to the drug store and pick up some baby gas drops called simethicone and give him a dropper as he may be gassy from the cheese from yesterday. Dogs are lactose intolerant and he may be having a bit of a reaction to it this time. If it is gas this should help. Again, if he doesn't improve by tomorrow he does need to be seen by a veterinarian.
Let me know if you would like more information.
A Voice for Your Pet
15 years experience in small animal medicine