Allergies are possible but not the first thing I would think of in a 13 yr old dog. A foreign body is definitely possible. I would also worry about a tumor, especially in a older large/long-nosed breed dog (they are more prone to nasal tumors). There is also a nasal mite (Pneumonyssoides caninum) that is probably more common than we realize--response to treatment (ivermectin injection) is diagnostic.
How are her teeth? Dental disease (oronasal fistulas) can also cause sneezing.
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