Noro virus survives stomach acid just fine. Influenza viruses can be detected in feces. E Coli bacteria infected with a Shiga virus/phage are stomach acid resistant and as few as 10 of virus-infected bacterial cells can cause infection. And then there's a roster of bacteria, fungi (ie yeast), and protozea (ie Campylobacter) that survive stomach acid.
The question is, can you infect yourself with a pathogen present in your own snot? Yes, you can. For example, about one-third of the American population carries staph on their skin or in their nasal passages/sinuses yet they don't get sick. Should you however get the staph in your bloodstream, or if your immune system is compromised, the risk of infection becomes considerable. It is possible to get sepsis from food poisoning.