I'm at a loss for the smell; I'm assuming you meant she smells like "throw-up". Wyorp Rock, could she be dealing with impacted crop turned sour crop?
Keep her hydrated if nothing else and continue to follow Wyorp Rock's advice. I know you said you "won't force feed", but you might have to do that to keep her alive until you can get to the bottom of what's ailing her.
Here's a link to a good primer on anatomy of the chicken mouth/throat and how to administer liquids (water or medicine) safely:
https://bitchinchickens.com/2020/02/06/how-to-safely-give-oral-medications/
You asked about what to feed her, but I'd not worry so much about feed right now. Make sure she stays hydrated; that's critical right now.
Keep her hydrated if nothing else and continue to follow Wyorp Rock's advice. I know you said you "won't force feed", but you might have to do that to keep her alive until you can get to the bottom of what's ailing her.
Here's a link to a good primer on anatomy of the chicken mouth/throat and how to administer liquids (water or medicine) safely:
https://bitchinchickens.com/2020/02/06/how-to-safely-give-oral-medications/
You asked about what to feed her, but I'd not worry so much about feed right now. Make sure she stays hydrated; that's critical right now.