Ds1 started doing similar when he was 8. With him it's reflux, which was initially caused by gluten intolerance - in fact we've been told to treat him as coeliac, because although his blood test was negative (he'd just had a norovirus bug and didn't eat anything for over a week, let alone enough gluten for the test) his food diary showed a clear correlation between symptoms and gluten intake and the paed felt it was severe enough to go completely gluten free.
He has now been gluten free for almost two years, but still get's reflux when he is stressed.
His reflux presents exactly the same way as your daughter, nausea, plus small pockets of vomit being brought back at mealtimes.
He doesn't have medication for it, because he hates Gaviscon and other than going the route of acid inhibitors, such as omeprazole there isn't really much else on offer. Omeprazole etc aren't appropriate because the reflux is episodic, rather than permanent. Apparently they used to prescribe chewable Rennie for it, but the drug guidance changed and they no longer do that.
If she's not eating for long periods of time, the acid will build up and make it worse, causing the nausea and then the mini-vomits when she does eat. Breakfast is really important - preferably something like porridge (ds has gluten free oats for his) that takes a while to digest.
Fatty foods will exacerbate it, as will anything too spicy and/or over-stuffing herself.
I can understand why she's making the association between eating and being sick and therefore the logic of not wanting to eat, but little and often throughout the day, starting with breakfast, is the way to go.
As for feeling sick when presented with food, it is actually possible, because the sight of food provokes stomach acid production, which - on an empty stomach - will trigger the whole cycle.
Could you perhaps try her with some low fat, neutral food to start with, while she builds her eating back up - thinking perhaps fat-free yoghurt or similar?