Was going to mention possible reverse sneezing
too, not uncommon in
Your dog is a mix but I suggest you do a Google search on each breed to see what health issues they can have, might help you out.
Often the National Breed club web sites will address health issues also and give you some insight.
If you are treating for Giardia, good thing that was discovered. Often does not show up in every stool. Make sure you wash the bowls daily in hot, soapy water or diluted bleach.