Get the kitty checked for dental issues, swelling in lymph nodes and a thyroid check. The swallowing issue may be a strong clue to treating her and get it done as soon as you can. Iv nutrition or fluids may help. If you can find a vet that is specific to cats , that may help but go online and kind of check to see if you can find someone with some good reviews. Also make sure food is actually swallowed if you can tell. Sometimes it can stay in their mouth or cheeks. Soft or liquid nutrition might be easiest. Thin liquids may or may not be easier. Did you try the gel or even unflavored yogurt? Just tiny licks at a time. The Pedialyte dilution needs to be given very slowly and carefully so she doesn’t choke. Even if it’s just drops at a time. There are other things that can be causing this. Since the vet just agreed with you, I’d want another vet to see her. Don’t give up until you have better information.