You don't generally see or feel significant external swelling with egg binding. Have you done an internal exam to check for a stuck egg?
How did you check for swelling and did you compare to a healthy hen. I find the best way to assess any abdominal swelling it to cup my hand between their legs from behind whilst they are roosting at night and check healthy birds on either side of the sick looking bird to get a direct comparison. Feathers can hide a lot but it should be pretty obvious to feel if they have some significant swelling or bloat.
If her crop is so full of fluid that she is refluxing then that suggests a major blockage or impaction somewhere in her digestive tract rather than just sour crop. If there is no obvious lower abdominal swelling or egg binding then the crop or gizzard are the likely locations and since there is little or nothing that can be done about a gizzard impaction your attentions can only be targeted at the crop.
If the crop is full of fluid which is refluxing then it may be necessary to empty it a bit before you start treatment because otherwise there is a risk that she will aspirate anyway. I vomit a chicken by holding it in front of my chest with the left side of the chicken nearest to me and then lean forward so that we are both upside down together the right side of the chicken's mouth is lowest. This way the vomit is more likely to drain out of the chicken's mouth than into the trachea and I can monitor the bird closely whilst I hold her against me and I can easily stand up to right both of us for a breather. Once she has regurgitated some of the fluid and had some room for manoeuvre in her crop, you can give her a little monitstat (don't dilute it) and massage. I try to massage 3-4 times a day for 10-15 mins each time.... this is in an upright position, not in the inverted vomiting position. The bird should be penned separate with no access to any fibrous material like grass/straw/hay etc and only given homogenous liquid feed that would pass through a kitchen sieve.... chick crumb mixed into plenty of water and left to become mushy is as good as anything. Many people have success using solid coconut oil to help break up and lubricate an impaction and I am told that birds will readily eat chunks of it in solid refrigerated form. If after a day or two of massage with coconut oil, the crop has still not emptied, then a stool softener like Dulcolax (without stimulant) can be used.
Please try to rule out a lower abdominal impaction which would normally be indicated by some abdominal swelling before embarking on the above treatment.
Good luck.
