Sounds like anxiety. Mild nausea and loss of appetite are something that I deal with on a daily basis. If you are happy then it could just be nervous excitement, like having butterflies in your stomach.
Yeah, OP didn't say how long they'd been together but if it's a new relationship after 3 years of being friends, especially if they're young and/or there's been lingering feelings for some time before becoming "official", then anxiety and nervous excitement is likely to be high!
If nothing else is triggering it then my advice would be to cherish the feeling while it lasts! Go on dates that don't involve food for a while or stick to lighter food that doesn't involve sitting in a restaurant to eat. Once things start to feel more normal between you then you can try formal meals again.
If she's suggesting restaurants in the meantime then just be honest with her, she'll likely find it sweet and endearing and it'll help to calm the nerves.
Cooking together can be a fun "date". Do it at your place so you won't feel so much anxiety. Or if you need food that badly after a couple hours make some popcorn and eat it while you watch a show or movie.