Sounds to me like she has had both sour crop and impacted crop as one can tend to cause the other. For example impacted crop is when the food in the crop cannot empty as it is blocked, which can then resolve itself, but the food having remained in the crop for so long can start to ferment, causing sour crop. When you say it looked like she was trying to throw up, was she stretching or shaking her neck and opening her beak wide? Because this would be a common symptom for crop issues, particularly impacted crop, as it is a chickens way of trying to shift the food in their crop to get it to empty. One way to tell whether she has a completely impacted crop is whether she is passing droppings, as if she is not this means no food is getting through her crop.
You do need to isolate her and getting a cage is good, but I would say you do need to separate her immediately from any food and preferably water too for 24 hours. If her crop feels solid you should give her some olive oil which will help lubricate food going out of the crop into the proventriculus, and massage her crop every few hours. If her crop feels squishy you should give her apple cider vinegar as this is a natural antifungal which helps with sour crop. These can be given with a syringe into the side of the beak or if you have no other way, mixed with water, but definitely no food. After 24 hours, water should be reintroduced and non-solid food can be given, such as scrambled eggs, layers pellets mashed up with water and olive oil, or yoghurt. Yoghurt is particularly good for sour crop as it is a natural probiotic that will help reintroduce healthy gut bacteria.
Once her crop has gone back to normal size and she is eating and drinking normally, she can be put back with the flock, but keep an eye on her as chickens that have had previous crop problems are far more likely to get them again, often due to loss of muscle tone from the crop being overly stretched (e.g. pendulous crop). Also occasionally crop problems can be signs of other underlying issues internally, so just be sure to make sure she is behaving normally.
If there is no improvement in her crop size after 48 hours I would absolutely recommend veterinary treatment. Additionally if there is a smell from her beak, white spots on the inside of her mouth, or any fluid comes out her beak, these are signs sour crop may have progressed to a more serious stage and veterinary advice would be advisable. Additionally if she will not eat any food after 48 hours, she should also be taken to a vet. I realise vets which treat chickens are hard to come by and expensive, but at that stage it would be the best thing for her.
There is some useful information about crop problems
here (bhwt website) if you have not already seen it
I really do hope she is ok and wish you the best with treating her!
