This is an interesting question. Food indirectly can affect things like if you don't get enough potassium, you then can get dehydrated and this causes drying that leads to potential nose bleeds. But it is a bit of a stretch that this is happening and she's only gotten the nose bleeds two or three times. I'm not sure the not eating correlates to the nose bleeds. This article talks about the main reasons someone gets nose bleeds. Take a look (copy and paste). https://www.webmd.com/first-aid/causes-nosebleeds
I'm guessing along with the above that the not eating breakfast was a coincidence and the nosebleed was caused by allergies that arose during the time she was sleeping or to something after she woke up. Some years ago my wife bought some new bedding and I've been allergic to the bedroom ever since and we can't for the lives of us recall what it was that was new. It gets worse the longer I'm in bed, though sometimes the problem doesn't arise at all. Allergies and the ensuing nose blowing can cause nose bleeds. As for dry skin inside the nose, very hard to fix permanently. Most of the stuff you could put in there would probably promote sneezing just by being in there, and the stuff docs recommend actually dries out the skin even more and causes more bleeding (they usually recommend vaseline, which shouldn't be used anywhere on the skin). That's my guess.