Thank you for the additional information.
I am very sorry to hear that her nose is so swollen and she is uncomfortable at this time. A sting from an insect can definitely cause an allergic reaction on a dog's nose. Sometimes the allergic reaction can also develop a secondary infection and quite a bit of inflammation therefore I would be concerned that she is starting to get an infection which is why her nose is more painful
At this time, I do think that giving her more Benadryl is safe. The dose of Benadryl for an allergic reaction in dogs is actually 1 mg per pound every 8 hours therefore you can give her a much higher dose very safely. Benadryl is a safe medication i dogs that rarely causes any side effect other then some mild drowsiness.
Since her nose seems inflamed and painful, you could also give her some over the counter medication for the inflammation/pain. The safest over the counter medication would be aspirin. The dose is 5 mg per pound every 12 hours. Even though this is safe some dogs can develop an upset stomach
therefore if you see any vomiting or diarrhea then I would stop the aspirin. Aspirin is also safe to use with the Benadryl.
If she will let you, I do think that it is a good idea to place a cool rag on her nose also as you were trying. Applying the antibiotic ointment every 8 hours can also be helpful.
If this is not helping, then unfortunately he really should be seen by a vet as he may need an oral antibiotic to clear out the bacterial infection on his nose.
Hope this helps to answer your question - if not or if you have any more questions please feel free to reply by clicking on the "reply to" button. Thank you for your question!