Sounds like food poison, or maybe just got a bug. Poultry poisoning can be deadly, but you sound like you're doing OK (on neo-geo.com). A lot of the time food poison from chicken can resolve and you'll be OK. Your body would probably tell you if you are on the verge of death. Red meat is the real deadly one. It can really eff up your heart, even if you think it passed, it can do permanent damage years later.
Basically you follow the BRAT diet when you can't hold anything down.
Banana's
Rice
Applesauce (plain, no cinnamon)
Toast (dry)
Those should keep you from spewing. I find when a bug hits me bananas are my go to. I can just leave them by the couch and roll over and grab one without getting up.
As for hydration, you can try sipping water. But it's hard to get hydrated that way. And not a guarantee you will get hydrated.
You want Pedialyte. Sold in the baby section. You can keep that down pretty easily. Or get IV fliuds at a hospital. But do NOT drink water if you can help it.
If you start cramping, that's the red flag to get to a hospital and get IV fluids.
I got pretty sick about 7 years ago, and basically vomited, and shit water for about a week and a half straight. I was miserable. Then I went to the ER for the first time ever on my own will, got IV fluids, and felt like a million bucks.
It doesn't sound like a medical emergency, but I would make a dr appt at the very least to give a stool sample and make sure there's nothing evil in there. If you feel better by the time it comes around just cancel. You don't want to be in a situation 5 days from now where you can't get in a dr, are cramping, and have to drop 2K at an er. Just make an appt now.
Also, about the fever. Keep it under wraps. 103 degrees is the danger zone (where your brain literally begins to cook itself). As long as you can keep it under that you should be good. Try and hold something down for a bit so that medicine has time to dissolve.
Also, when you have a fever hot showers and bundling up in blankets sounds like a good idea, but it's not. You're not cold, you're actually burning up. You need to just use a sheet instead of a hoodie and blankets. This will help you break your fever faster, although it sucks being cold. So make a decision, be cold and get better faster, or feel warm and miserable longer.
Good luck.