When you are sick, you often just don't have an appetite. You will never know if her throat is sore, or she has sinus pain, or is also teething with a headache.
Right now, she needs fluids and only fluids. Try to calmly offer her normal feedings plus an extra feeding every few hours (in a different location if possible). Read a story during the feeding to distract her.
If she doesn't take her regular feedings, I would offer her some wet things to eat (since she has been on solids for a month), such as a piece of watermellon, or similar fruit.
If she doesn't gnaw on that, offer a wet washcloth. Or wet her hands, and hope they get into her mouth.
Give her a nice long bath tonight, and encourag her to chew and drink from some plastic cups/spoons/toys/washcloths.
Hope your little one feels well again soon.