Now the concern in this situation is that her lameness may be muscle strain/sprain related, but as she is quite young there is the risk of fracture here. If it is the former, we should see her progressively bear more weight on the paw as the shock of injury fade. But if we have a fracture, they usually won't improve with rest and time.
Unfortunately, you will be limited with what you can do here since OTC human pain relief treatments are all toxic to cats (some fatally so). Therefore, further to the cool compress, your mainstay here will be to rest her and limit her ability to walk on this. To do so, you may need to restrict her to a room where there is nothing she can jump on/fall off. Or you can even keep her in a cat carrier with food and water overnight (though we'd remove food after midnight so she has an empty stomach in the morning --just in case her vet needs to xray this paw without delay).
Now you noted that she wasn't keen to eat. This can be shock or pain related, but we do want to keep tempting her. If she isn't keen on her usual food, then you can offer her boiled chicken, boiled white fish, cottage cheese, scrambled eggs, or meat baby food (as long as its garlic/onion free). If she were to become dull or show weakness from not eating or having a low blood sugar, that can be boosted by rubbing a sugary syrup on her gums (ie karo syrup, honey, pancake syrup, etc).
Overall, you are on the right track here with Rosebud. Though we are limited in what more we can do at home. Therefore, the above would be our mainstay here at this point. Otherwise, if she seems very sore, then we'd need to consider having her seen sooner for at least cat safe pain relief (ie Metacam) to reduce her discomfort and tissue inflammation.
Please take care,