I accidentally got tap water up my nose and it dripped down the back of my throat while taking a shower. it's enough to irritate my nostril and throat. how likely is it i will get a bacterial infection or a brain eating amoeba? i live in the us?

Almost zero chance. This sort of thing happens millions of times every day and almost nobody develops a health problem as a result.

There is NO apparent risk of an infection acquired in this fashion. Your apparent concerns raise questions about future coping with medical concerns. You might consider obtaining some counseling to assist future comfort.