Is it normal for a shih tzu puppy to snort while teething?
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perhaps the pup is doing a thing called reverse sneezing(there are some postings on the forum somewhere about this condition) which a lot short nosed dogs get, my boston has done it since she was a pup, though not so much now she(just over a year now) used to snort so much people used to think she was dying but if you just cover the end of thier nose it makes them gasp for breath it is all to do where the soft palette gets hooked over the larynx another way to clear it is just very very gently breathe in the pups mouth this is what i do to mine abeit the strange looks but it works

Yes it is very common for shiddies to do this when teething. Mine did and so did everyone else's that I know. My little chap did it a few times after teething but eventually has grown out of it. He's now 3 yrs.