My Willow has allergies, and she sometimes sneezes. Stress can cause all kinds of things in cats...whether that is causing new issues or amplifying existing ones. One time, after I took Willow for a quick trip to the clinic just for them to get blood to test, her eyes started running. Her eyes had never run before, and she was 15. I asked about it and was told runny eyes are common in cats and can be caused for many reasons and not to worry about it. That was not an answer I liked. It killed me to see her pretty eyes running knowing that something about that vet visit caused it. It took a long time for that to stop, and really, she still gets a little crusty spot next to one eye.
A lot of times, vets blame any kind of allergy-type symptoms on herpes and want you to give the cat something like Viralys. For Willow, that is not her issue. I humored a vet once and gave her Viralys for awhile, but it had no impact at all. She has always been prone to allergies, she even has asthma. I started giving her 1/4 of a 10mg Zyrtec every day, and it seems to help a little with the allergy symptoms (also increases her appetite some which is a good thing).
There have been a couple of times when Mia had a little sneezing fit which was very weird since she normally does not do that. It only happened those couple of times and has never happened again. Maybe that will be the case with Jack.