Hi there...sorry to hear that your dog is not well. This sounds like a very frustrating problem! It sounds like your vet is doing all of the right things. It looks like we are trying to find whether there is something stuck in her throat.
Has she had a thorough oral exam under anesthetic? That would be my next step. I would want to examine each of her teeth and all of her mouth and as far back into her throat as possible. Ideally, an endoscopic exam of the esophagus would be great, but not all vets have the equipment to do that.
Another thought is that she may have a condition called laryngeal paralysis. When this happens, the larynx doesn't open all of the way and it becomes difficult to breath. The way to diagnose this is by administering a light anesthetic and watching her larynx open and close. There is a surgery to fix this, but it is often expensive and can have side effects.
If you have financial constraints you could ask your vet to prescribe some antibiotics (in case there is a foreign object causing an infection) along with some bronchodilators to help with the breathing.
I hope this information helps! If you have more concerns, then hit reply. Or, if my answer is sufficient please hit accept. I'm in appointments this afternoon so I may not be able to respond immediately. Thanks!