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Hello - I am Dr. Matt - I would be glad to help you with your question.
I am very sorry to hear that Doodle was nipped by your dog. Swelling, like you are seeing on her face, is very common as most dog bites can cause quite a bit of inflammation and infection. I am glad to hear that she is eating, drinking, and playing well as this is an important sign that she did not develop any serious injuries to the bones of her jaw or eye. A compress is a good idea as this can help reduce swelling and inflammation. Most likely she does not want you to do this anymore though as the swollen area is infected which can cause it to be quite uncomfortable. Therefore, this could get much more serious if left untreated especially due to the area in which the swelling exists. At this point, she really does need to be started on an oral antibiotic such as Clavamox as the infection under her skin can get worse causing a fever and making her feel very lethargic. Clavamox can not be purchased over the counter though therefore I would recommend taking her to your vet as she honestly does need to be started on this medication right away. In addition to the oral antibiotic warm compresses are better then cold as the warmth with help drainage of an pus or bacteria that may be trapped under the skin. If she still will not let you place a warm washcloth or towel on her face then you do not have to stress her out with that though it is definitely worth trying again.
Overall, a bite wound on the face can be serious as it is most likely infected which can cause quite a bit of discomfort for her.
Hope this helps to answer your question - if not or if you have any more questions please feel free to reply. Thank you for your question.