I will give you the standard advice for vomiting. Withhold food and give water only for eight hours. If he can't even hold down water initially, then withhold water for eight hours. After he is holding down water, try chicken or beef broth. The best broth is home-made bone broth, but if you have to use canned broth, it is okay. Some dogs will drink Pedialyte or Gatorade in place of broth, which is also okay, but mine won't drink it.
After he can hold down broth (or if you didn't have any broth, after he has been holding down water for at least eight hours), try giving him SMALL amounts of low-fat, easy-to-digest food, like cooked white rice, cooked lean meat, or hard-boiled egg. At that point, when he can hold down a small amount of easy-to-digest food, you can try giving the sucralfate again.
After he is keeping small amounts of easy-to-digest foods down, you can gradually increase the amounts, and when he is holding down a full meal of those foods, then you can gradually transition him back to his regular dog food. At four months, he can go a day without eating, so I wouldn't worry about the initial fast. If he can't even hold down water after he's had nothing on his stomach for eight hours, I would call the vet.
I'm thinking it might be the new antibiotic, rather than the prednisone that is causing the vomiting. A lot of antibiotics cause vomiting, and I've never heard of prednisone doing that. The dilemma is that you really need to finish out the course of antibiotics, if at ALL possible, in order to avoid cultivating resistant bacteria. Due to that issue, you might need to call the vet anyway. If you are in the US, then we are just starting a four-day weekend, and it might be good to get some input as to what to do about the antibiotics. Otherwise, you're waiting until Monday, and that is a long time in this situation. You also need to know what to do about the prednisone, since sudden withdrawal can cause symptoms. I don't know if the two or three days that he was on it was enough to cause that kind of problem. So maybe you really do need to call the vet.
Here, we have emergency veterinary clinics that you can go to over the weekend, if necessary. The especially good thing is that the ones in our area will give you free advice over the phone to help you decide if you really need to come in or not. You might check and see if you have any kind of local resource like that.
Puppies are like kids in some ways. It almost seems like they plan these things for the most complicated time, like on a weekend or holiday. Get him through this episode, and things should straighten out for a while. Good luck, and let us know how he does.
You can also try letting him lick a Popsicle for hydration, like when they give human patients ice chips in the hospital. I've never had that cause more vomiting.
Thank you so much for the advice. We will try all of that.
Yes couldn't be a worse time than going in to a 4 day weekend. If he is still not doing better tomorrow we will find a vet that is open. Thanks again.
I know it feels terrible to deny food and water to a sick puppy, but that is the only way that the stomach can rest and recover. Again, good luck, and Aloha yourself!