This is called gaping, and it often indicates a respiratory infection. One thing you can do right away to help her is to make sure the temperature in her enclosure is kept at 85 to 90 degrees day and night. While it's usually recommended that the temperature be lowered at night, when they're sick, it's better to keep them warm all the time. This link talks about that:
Also try misting her enclosure twice a day. It may not be humid enough for her.
At any rate, the "gaping" of the mouth is often a sign that a respiratory infection has advanced. There are also a couple of other diseases that can cause gaping, such as mouth rot. Look inside her mouth for any growths, cheesy-looking discharge, or discoloration. Regardless of whether it's respiratory or something else, she will need to be seen by a veterinarian who knows about reptiles. A respiratory infection can be caused by bacteria, fungus, or a virus. Sometimes it's necessary for a vet to do a culture to determine the proper medication. There are times when two or more drugs must be administered at the same time.
I don't know your location, but here's a link that has a directory of reptile vets by state:
I wish I could tell you a cure you could administer at home, but I don't think there is one. This is a serious illness that can easily be fatal. A reptile specialist should be able to determine what's causing your dragon's illness and get her started on the road to recovery.
I hope you're able to quickly get a diagnosis and cure.
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