-- First, most importantly, since you are not equipped to perform surgery which may be necessary, find an urgent care facility within 2 hours of you and be ready to go. No matter what.

Also, just because you might not see "avian vet" along with DVM doesn't mean they aren't experienced with birds. Call every vet in town - one will at least be able to recommend someone.

If you have a Pet Smart in town you have a bird vet right there; 7 days a week. They have a clinic inside that sees just about all animals, including small birds.

---
Pet Co keeps a list of names of bird treating vets - call and ask.

---
OK, with that said, here's what you can do in the meantime: Put a dab of corn syrup or maple syrup at the side of her beak where she'll lick it off. Offer a drop or two of plain water this way as well.
---
You can try swabbing her vent area with a bit of KY jelly or other lubricant (not Vaseline) – even regular cooking oil is ok in a pinch, but since you've done that, hold off on doing it again.
---
Set her in a shallow pan of warm water (not hot) – this might relax the muscles enough to pass the egg.
---
Bringing her into a hot, steamy bathroom while trying to keep her calm and going through the shallow, warm water bath and vent massage - while finding a vet to see her urgently is another option.
---
Put a heat source in her transport carrier or box lined with layers of newspapers, old tee shirts or smooth towels. An easy and reliable heat source is a ‘rice sock’. Fill a thick, clean sock about ¾ with raw rice and knot the end. Heat in microwave for 1 ½ to 2 minutes and shake it out afterward to distribute the heat evenly. Lay this on the bottom and cover with a few layers of newspaper or cloth - it’s a moist heat that may even help the egg move.
---

You don’t have much time - find an urgent care facility and go now. It’s far better to be driving two hours to the nearest caregiver rather than trying to wait this out.
---

She may not only face a life threatening situation here, but this is a common cause of paralyzation in birds. Sometimes permanent.

---

You have my prayers!