Thanks for the answers to my questions although I'm sorry that I was off my computer when you responded back.
I can understand why you might think she got into something toxic given the sores on her mouth but in most cases, these patients aren't going to be sneezing. I wouldn't completely rule it out but it's not just as likely. When both symptoms are present (with or without a nasal or eye discharge), then I'd want to rule out an Upper Respiratory Infection (URI) caused by a calici virus.
Herpes is the most common cause of an URI in cats but the mouth and mucous membranes aren't usually affected. When the underlying virus is Calici, then ulcers can develop on the nose, tongue and surfaces of the mouth which are very uncomfortable/painful. These cats will often drool or show disinterest in food if severe enough. In addition to antibiotics (there's often a secondary bacterial component when a URI is present), I'll dispense pain medication such as Buprenex although every vet has their preference.
Cats with URI's sometimes run fevers as well which might account for her lethargy. If you can take her temperature (not always the easiest thing to do in a cat), normal is between 100 and 102.5.
Most uri's will last about 10-14 days in case you were wondering.
Supportive care is critically important for these patients especially when they're older. Force feeding is often necessary if they aren’t eating. You can mix canned food (or human baby food but avoid onion and garlic formulations) with a lot of water in a blender and use an eye dropper or syringe to squirt some of this liquid into the side of the mouth where there's a gap.
Three days is longer than I'd like to see her go without food so I'd start the above as soon as possible.
Probiotics such as Forti Flora have been shown to help many of these cats with URI's; probiotics aren’t just useful for gastrointestinal issues. This particular product is available as a powder which is sprinkled on the food every day for those cats who are eating or mixed in with the canned food/water mixture that I mentioned. It can be purchased at many pet/grain stores or online.
I hope this helps although, again, my apologies for the delayed reply. Deb