Unlikely. Your nose hair is designed to filter the fur from going into your lungs. If your pet sheds a lot, you may want to get a pet comb to brush them.

I’m no expert on the human anatomy but I’d say dog hairs are too big to make it that far. Maybe pet dander could find its way if it’s fine enough but hairs would probably get caught somewhere either in your nose or throat beforehand.

If it were the case we’d probably be full of hairs by the time we’re in our mid youth. Or I’m completely wrong and our lungs somehow rid of hairs or other larger debris naturally!

Pet groomers can get something called groomers lung which is when teeny tiny bits of cut hair and pet dander get in lungs and don’t get swept out by the lungs cilia because they are sharp edged from being cut/trimmed they lodge in the lungs and cause problems by damaging and scaring the lungs or by causing an allergic reaction directly inside the lungs. This is usually a chronic condition once it develops as the lungs are permanently damaged. This is prevented by keeping the workplace clean, well ventilated and wearing a mask when grooming dogs. Natural dog hair that isn’t being clipped should be too big to be easily inhaled into the lungs, if any does get into your airway you’d most likely cough it out or swallow it and digest it.

I’m not an expert, per se, but I think we covered enough anatomy in our first year of medical school for me to answer with some modicum of authority.

The structures of the bones, hairs, and membranes of your respiratory tract are able to prevent microscopic particles and single-celled bacteria from making it into your lungs. Pet hair cannot get into your lungs passively, and your sneezing is from the microscopic dander irritating those structures. Your mom seems to be grasping at straws or retelling old wives’ tales to express her personal distaste for the animals. The worst that can happen here is an allergic reaction, which doesn’t seem to be applicable to you.