1. Rats can't throw up, this is why she never throws anything up.
2. It is probably not something stuck in her throat, sounds like a respiratory disease.
Rats get these a lot. It's common in rats from pet shops because they are not specially bred. Even rats from a breeder could have myco. It's a common disease that affects the breathing and lungs.
The wheezing is not always present but it sounds sort of rattly when it does come on, usually in the morning or at night.
If your rat has a resp. disease she will sneeze often and make sort of snuffley noises a lot. Sometimes it will sound worse than others.
You should get your rat checked out by a vet who will prescribe Baytril to sort the problem. It's a pretty general antibiotic but will need to be given in the right dosage. Your vet will weigh your rat first to find out how much she needs.
Hope this info helps.
Try looking rat respiratory diseases up on the internet to help you compare your rats symptoms with those of diseases such as myco.