Good evening - I'm Dr. Sara. I'm a licensed veterinarian who works exclusively with cats and dogs. I'm sorry to hear that Sophie isn't feeling well today. I know that it's scary and stressful when they become ill suddenly like this.
With an acute (sudden) onset of vomiting in a kitty, it could be that she's either caught something infectious (think stomach flu) or that she's eaten something that didn't agree with her. When I have pets who are vomiting suddenly like that, I suggest not offering any food or water for 8 to 12 hours. If they're still not interested in food or water after that amount of time, they should be examined at the vet's office and treated. They may only need some anti-nausea medicine to get them feeling better, but there's unfortunately nothing available over the counter that's going to be helpful. If they are interested after their fast, I start by offering a small amount of water. If they hold that down for two hours, I move on to give about a teaspoon of food. As long as they continue to keep their small meals down, then I gradually space out the feeding and offer more at each meal. If they begin vomiting straight away with reintroduction of food, then they need to see the vet.
A third potential problem we can see cause severe vomiting in kitties is foreign body obstruction, which is where they've eaten an object that is obstructing their GI tract. Pets with GI foreign bodies do not improve with any type of supportive medical care - they need surgery to relieve the obstruction.
As an older pet, unfortunately I have to add diseases like kidney or liver failure to my list of potential culprits. I'll typically do a blood panel to check organ function on a kitty who is either very sick or not responding well to supportive medical care.
Please keep me updated on how she is doing and let me know what follow up questions I can answer for you.