Do Amun's episodes look like this (this is a video of a dog but the episodes will be similar in dogs and cats)?
If she looks like the video this is a "reverse sneeze" which is caused by irritation of the pharynx. It can be from inhaled irritants. It can be related to gastroesophageal reflux. It can be caused by excitement or post nasal drip or an overlong soft palate. It 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 her throat.
In Amun's case because we know she ate some rubber pieces I suspect that this is related to gastroesophageal reflux and stomach acid burning her pharynx and upper airways/back of her nose.
I am worried she may have an obstruction.
If she doesn't have an obstruction, but just an upset stomach/reflux from eating something she should not have then using an acid reducer may help. You can try Pepcid-ac (generic famotidine) at a dose of 0.5mg to 1.0mg per kilogram orally every 12 hours for a few days. That's one quarter of a 10mg tablet per 2 to 5 kilogram cat every 12 hours. If this helps she can stay on it for several days as Pepcid is quite safe.
In cats this may just be postnasal drip and pharyngeal sensitivity from an upper respiratory infection. In these cases you may see eye & nasal discharge as well. As the infection waxes and wanes her symptoms should improve. If this is related to a respiratory infection you can try supplementing with L-lysine at 500mg orally twice daily. This amino acid interferes with virus replication and thus decreases the length and number of recurrances.
Sometimes this can be related to dental or gum disease and the secondary inflammation from chronic infections. That would be very unlikely at this age.
In cats this can also be a symptom of asthma or even heartworm disease. I would recommend a heartworm test and chest radiographs to ruleout these disease processes if the symptoms persist.
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