Does your wife have a history of cold sores?
Your daughter's symptoms sound consistent with oral HSV, but your doc is right - it could also be other things. However, I'm quite surprised they didn't swab the blisters. Since it's been less than 48 hours, I'd go back right away and get them swabbed for a PCR DNA test for HSV - make sure you ask for type-specific results.
The caveat: lots of kids get cold sores when they're kissed by family members. Your little girl would hardly be the first. It's quite common. Best to you!
I would get a second opinion. My oldest son had something very similar last year and it ended up being cold sores. Started out small and he kept picking at them because they bothered him then spread to his cheeks in a rash.
Maybe take her to the emergency room. Can get a faster opinion that way and ask they do a swab to test the sores. Best of luck. Hope she feels better soon!