That's a tough one...the feeling-hungry-but-still-want-to-chuck situation! At that stage of a hangover I don't think your body really knows what it wants. Maybe try a very small amount of some fatty, greasy, shit food (like one bite) and take it from there? As a general rule, IF you can get it down, you will feel better quicker! If all else fails...I have found that laying 100% still and not moving for a very long time (like a day) is also quite effective,...even if a little unpractical
If in doubt, just get drunk again...and deal with it tomorrow instead!