A reverse sneeze is the body's attempt to clear irritants from the nasopharynx or back of the throat and would be considered a normal reflex to any nasal, pharyngeal, or sinus irritation.
When a dog only occasionally reverse sneezes, then I don't worry about it too much but when the condition becomes chronic, then the following explanations which I list below are possible causes. It's a little unusual for a dog this age to start this behavior, though; typically it's seen in younger dogs.
1. Nasal mites but may be difficult to find.
Treatment is fairly easy, though, with Ivermectin given every week for three doses.
2. Foreign bodies such as a blade of grass or foxtail. Often sedation with rhinoscopy is needed to detect such a problem, though.
3. Allergies or rhinitis/sinusitis which may be more challenging to diagnose without advanced testing but response to medication can sometimes help to rule this problem in or out.
4. Polyps or masses which are best diagnosed with an MRI and possible rhinoscopy and resultant biopsy.
5. Unknown...which is often the case with younger dogs.
6. Lower airway diseases can result in secretions that are coughed up; these may irritate the nasopharynx resulting in a reverse sneeze.
But, usually these patients are also coughing or showing other signs.
As to at-home, over the counter treatment options, I often suggest that owners try antihistamines such as Benadryl (Diphenhydramine) which can help to dry up secretions which may be triggering this behavior. The dosage would be 1 mg per pound of body weight twice a day although sedation can often be seen as a side effect.
If Cotton doesn't respond to antihistamines and she were my patient, I'd probably treat her for #1 just to eliminate it from the list...but every vet practices differently, of course.
I hope this helps. Deb