Hi Allen. Welcome to permies!
If she “vomited up a thin watery liquid”, then for sure she has ‘sour crop’. Sour crop is a yeast (Candida) infection of the crop. It can be treated easily.
About the “runny brownish-yellow discharge”, this one is called ‘vent gleet’ and can be caused by many things- bacterial infection, yeast infection of the cloaca, or (rarely) parasites. A fecal test would pinpoint the cause of the discharge. But you said something very relevant, you “noticed a foul odor”. How far away was she when you noticed the smell? Because the difference between a discharge caused by bacterial infection and a discharge caused by an yeast infection is: the yeast infection really makes the bird stink. In a closed room, the smell is noticeable when you enter the room. In the open air, you know when you pick her up.
Conclusion: very likely she has a systemic yeast (Candida) infection, um, at both ends. How old is she? I had my first sour crop in a young hen who overindulged in mashed potatoes. The second was in an old hen, nothing specific about what she had eaten. My only Candida vent gleet was in a middle aged hen who had been suffering from salpingitis for a few days.
Treatment: can be treated at home with over the counter antifungal cream, like something containing MICONAZOLE. I’d recommend you duckduckgo or google ‘sour crop’ a little bit, to familiarize yourself with it, finding out the potential causes, etc. For the ‘vent gleet’, she needs a good
local bath and an application of miconazole cream around the vent and a little inside the vent, daily, for 2 or 3 days. For the sour crop, a question, is she still eating? She must be fed only things that don’t encourage the yeast, like plain active yogurt (no sugar!), maybe some cucumber, things like that, very little
feed or no feed at all. And then wait a little and see if she gets better. But if her crop is very swollen and puffy, and she stopped eating, then we
should give her some miconazole cream in her beak too.
Is she still eating?