Was she able to pass the egg?
Even though she has oyster shell for calcium you may need to give her some calcium to help her with contractions to get the egg out. I don't know much about quail so hopefully others will chime in...usually for a chicken a whole crushed TUMS can be given. So for your quail, I would try to give about 1/4 or less (1x a day until the egg comes out). Crush it and sprinkle it over some chopped egg.
If you have some Poultry Nutri-Drench give her some of that as well. About 5drops.
See that she is drinking well. Dehydration makes it worse.
Some causes of soft shell eggs include not enough calcium, vitamin/nutritional deficiencies, stress, illness or defective shell gland.
Since you do have vet care, you may want to consult them again - they may have liquid calcium they can give her or they may need to extract the egg. To help her stop laying, you can try placing her in the dark for 16hours a day, but this would not be a good idea long term. The only thing I know that could possibly help long term would be a Suprelorin Implant. This can be done for chickens, but again, I don't know if it's possible with quail.
I am assuming the reproductive system is similar to chickens, the worry would be that she begins to "not" expel the eggs and infection set in or egg matter starts to drop back into the abdomen causing Egg Yolk Peritonitis.
Just some ideas. Let us know how she is doing.