I hope this makes you feel better.
I am an aquatic biologist and used to survey for freshwater mussels regularly. I'm talking almost every day for 6 months. How did I survey for mussels? By snorkeling or free diving in freshwater. I did many many surveys in the state of Texas in particular, a state which has been known to have one of the highest number of cases of amoebic infection-related deaths in the country. So for 6 months, 6 days a week, I used to dive in warm, stagnant fresh water in Texas and yes getting water up my nose on a daily basis! Yet I am not dead! Since then I have not been doing mussel surveys much and my work is mostly above water now.
However I am just saying that I was at very high risk of contracting the infection, yet have not. You are not going to contract the amoebic infection from shower vapor. Think of how many showers you have taken in your life and remained healthy! If you want to irrigate your sinuses and put your mind at ease about neti pots and contaminated water, use a saline mist to irrigate instead. Arm and Hammer makes a nice one. It is a salt water solution and N. fowleri cannot survive in salt water.
Hope this helps to put your mind at ease!