Quite a number or problems can cause vomiting and diarrhea. For instance: He may have inflammatory bowel disease (IBD) or food allergy/intolerance. He could also have GI parasites. Vomiting without diarrhea can be caused by a number of illnesses including urinary tract infection, interstitial nephritis, hairballs, and even anal gland impactions, among others.
Going back to your vet to resolve this problem is best, of course. There are things that you can try at home until you get to the vet, such as: giving 5 mg of Pepcid twice daily prior to meals, and giving probiotics mixed in food once daily. Pepcid and a pediatric probiotic are both available over the counter. The probiotic is given by the weight of your cat as listed on the label. This can take 2 weeks or more to resolve the problem as your cat's gut repopulates with the beneficial flora.
Thank you very much. I am going to try those things until we can get back to the vet. I appreciate your help.