Hello, my name is***** and I have over 290 years of experience as a veterinarian. I'm sorry to hear that your girl is gagging and making strange noises as if she has something caught in her throat.
Is she able to eat and drink normally? If so odds are unlikely that she actually has anything stuck and the gagging and noises may be simply due to throat irritation or reflux.
Do your pup's episodes look like this?
If they look like the video this is a "reverse sneeze" which is caused by irritation of the pharynx.
It can be from inhaled irritants (like any sort of pollen).
It can be related to gastroesophageal reflux.
It can be caused by excitement or post nasal drip or an overlong soft palate.
It could be due to chewing and swallowing rough material such as wood or bones.
Dogs with dental and gum disease can have lots of inflammation and may be predisposed to post-nasal drip and reverse sneezing.
A reverse sneeze isn't harmful as it's just a spasm of the muscles around the pharynx because of the irritant, but it's no fun to watch. It can be stopped most times by rubbing the throat gently.
If it is because of gastroesophageal reflux then giving her an acid reducing medication may help. You can try either:
1) Pepcid-ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at a dose of one 20mg tablet per 40 to 80 pounds of body weight every 24 hours.
These will reduce stomach acid and should help decrease symptoms related to reflux. These medications are quite safe and can be used long term if need be.
If it is related to an overlong soft palate then surgery may be required eventually if this is interfering with enjoyment of life or leading to breathing problems.
You don't mention her breed but Bulldogs and other flat faced breeds are known for having a complex of issues that can make breathing more difficulty, called brachycephalic syndrome. These issues include an overlong soft palate, stenotic (small, closed in) nares, and parts of the larynx that evert out when breathing called everted laryngeal saccules.
If they have a low grade respiratory infection or are exposed to cigarette smoke, candle or incense vapor, pollution or other irritants then that can be a possible complicating factor as well.
Ideally if this is worsening your pup needs to be evaluated by your family veterinarian. They can determine whether this is related to a reverse sneeze or something more serious such as brachycephalic syndrome, and see how much she is affected and whether surgery to correct some, or all, of these problems would be beneficial.
If your pup has brachycephalic syndrome dogs that don't have these problems corrected surgically can suffer from exercise intolerance and easily suffer from heatstroke because they cannot breathe properly. Long term they can suffer from tracheal collapse and secondary heart disease from their struggle to exchange oxygen. If the abnormalities are corrected surgically the pup can have a normal life. Surgery is best done by a very experienced, board certified surgeon to have optimal results.
Here is a link to a webpage that discusses brachycephalic syndrome if you'd like more information: https://www.acvs.org/small-animal/brachycephalic-syndrome
In the meantime I recommend making sure your pup does not get overheated or exercise too strenuously.
If she starts to open mouth breathe then play should stop.
Because sometimes this can be related to dental or gum disease and the secondary inflammation from chronic infections. If this is the case a good cleaning should improve things tremendously.
If she chewed on and swallowed an irritant then using one of the acid reducer medications and a bland, soft diet may help.
A homemade bland diet consists of 1/3 boiled, lean hamburger (or boiled, white skinless chicken), all fats and juices drained off the meat, mixed with 2/3 boiled, plain white rice. Add low salt chicken or beef broth to make it softer. Feed several small meals a day. You might wish to add 2-4 tablespoons of canned pumpkin (not pie filling, just pumpkin) to each meal if you think she did ingest something sharp to help increase fiber, which will help push pieces through.
Feed this food for several days and if she is doing well then gradually start mixing in her regular diet, more at each meal. It should take about a week to get her converted back.
Please let me know if you have any further questions.