Thanks so much for the answers to my questions.
Based on the information you've provided, it sounds like Tilly may have an infected tooth....this is commonly called a Tooth Root Abscess which is basically pus that is taking the path of least resistance and creating an abscess on her face.
Some of these cats are still eating while others might be running a mild fever (and thus have a decreased appetite) or experience pain/discomfort when they eat so they have less interest.
A visual exam of her mouth might not reveal any abnormalities; usually this is determined under anesthesia or with dental x-rays.
Unfortunately, there won't be anything that you can give her over the counter for this problem. The best solution is to remove the tooth and treat with antibiotics although I know you'll be worried about anesthesia in a cat her age.
I will sometimes dispense oral antibiotics for these older cats with this problem (especially if they are anesthetic risks). If they respond, then I will keep them on a low dose of Amoxicillin for as long as necessary to control the infection. Obviously, this isn't the optimum solution but it's a practical one for many cats and their owners.
I realize that my answer may not be what you want to hear but I would be doing a disservice to both you and Tilly if I were less than truthful and honest in my response to you. I hope you understand.
I also hope that this is helpful and that you will have Tilly seen by your vet so that treatment options can be discussed. Deb