I agree about avoiding the ER, if possible, because of the stuff that goes around there, but if I were you I would call the pedi and ask if she can get some iv fluids there, at least. If she gets dehydrated, she will be listless and it will be very difficult to get her fever down. She needs fluids desperately. If she doesn't eat, I wouldn't worry. My son has gone days without eating and then when he's better he makes up for it.
Remember, the ear temp is going to be different than the others- there should be a chart or something inside the ear therm that says what is "normal" and it's a degree or two above what a different therm would read, I believe. We bought the temporal therm (like they use at the docs) and I believe it works best (though we usually take the average out of three tries). They're under $40 at Walgreens, if I remember correctly. I have the ear one too, but it doesn't seem to coincide with the Dr's office (ear is always higher). I mean, why would the dr's office say 103.6, then at home it's 106.1? The therm may be off and you're getting scared for nothing, you know? I would be real scared with a 106 temp, too.
Unfortunately the temperature almost always rises when they sleep- same thing happened with my son. It should go down within an hour or so of waking, though.
I would guess that she probably picked up a virus at the party and there's nothing much to be done about it, unfortunately. I feel for you- been there. It's the worst, seein' your little one go through all that.
Couple thing to remember on fevers- she'll want to be naked, but don't let her, cuz then she'll start to shiver and that can make the fever worse. Keep one layer on her (a sheet or t-shirt, shorts, whatever). She'll get hot and want it off, but it's not good. At least that's what I read.
Be prepared that you may not get a diagnosis. They'll probably conclude that it's a virus, as it usually is.
Sorry if I couldn't be more positive.