First welcome to YT and so sorry that Rascal is not feeling well. How is he doing? I, too, wonder if it's a reaction to the shots given together.

My vet gives them separately and we don't have to get some of them every year.
I hope that's all it is and that Rascal's tummy gets better soon. I know you are doing the right thing in not giving him his meds as he will just throw them up anyway and they'll be useless.
If he doesn't get better you should just call your vet again.
Keep us posted.