She may have a sour crop, from your description of the crop. You need to verify this by withholding food and water over night and checking the crop in the morning to see if it's empty. If the crop is still full and squishy in the morning, then you will need to treat for sour crop.
The good news is that this is likely what's making her sick. It's a miserable condition caused by Candida yeast, the same thing that women get in their vagina, and it's treated with the same medicine.
Get some miconazole vaginal yeast cream from the store. You will be treating her twice a day for seven days. Here's all you need to know about it.
https://www.backyardchickens.com/ar...w-to-know-which-one-youre-dealing-with.73607/
Giving her kefir is fine. In fact, it's a good thing to give her as she's recovering from any type of crop disorder, and also after you treat a chicken with an antibiotic to restore good microbes in the crop and intestines. It would be hard to overdo it, as chickens seem to self limit what they consume of milk products. Just be sure there is no sugar in it and don't give her any carbs during her crop treatment. Egg, tofu, yogurt, and kefir are fine.