Hello, I'm Dr. Deb and will do my best to help you today.
I'm sorry that Floyd isn't feeling well; given her age, I'm sure you're quite worried about her.
It's certainly possible that she's running a fever especially if she feels warm but it would be good to confirm if you have a thermometer. It isn't always the easiest thing to do in a cat but if you do manage to take it, normal is between 100 and 102.5.
If her temperature is elevated, then there are several possible explanations which range from a viral or bacterial infection to Fever of Unknown Origin (which is exactly what it sounds like) to auto-immune diseases...just to name a few possibilities.
Unfortunately, it wouldn't be advisable to treat her fever with any over the counter medications since to do so, might make matters worse (cats are sensitive to many of these drugs).
I do have an option for you to consider which may help with her nausea. Over the counter Pepcid AC (Famotadine) can be given although it should be used cautiously in geriatric patients and patients with significantly impaired liver of kidney function. I typically only recommend 1/4th of a 10 mg tablet once daily for older cats as opposed to twice daily for younger ones.
Keeping her hydrated will be important so if she's not drinking, you may need to supplement with Pedialyte or tuna/clam juice. One way to get fluids into her would be dribble a small amount of liquid into the side of her mouth with a syringe, eye dropper or small turkey baster.
I would also limit the amount of food she's allowed to eat at one time (if she's still eating). Chicken is one option or baby food (avoid those with onion or garlic in them).
If she continues to vomit and/or has a high fever, then a vet visit may be prudent. I hope this helps and that she's feeling better soon. Deb