I have read somewhere that if a person does not rinse his nose but pours water all over his body to the extent that no part of his body is left dry, then such kind of Ghusl is valid, according to the Shaf'i fiqh. However, I am not sure. I do not rinse my nose for the fear of Naegleria Fowleri amoeba.
Rinsing the nose in ghusl is obligatory according to the Hanafis and Hanbalis and a sunnah according to the Malikis and Shafi'is.
الاستنشاق ... وأما في الغسل للتطهر من الحدث الأكبر فهو سنة عند المالكية والشافعية، فرض عند الحنفية والحنابلة
If you are concerned about amoeba contamination then you may consider using a bottle of sterilized water (boiled or chlorinated etc.) for the purpose of washing your nose.
There are three main obligatory acts in order for ghusl to be valid. Rinsing out your mouth like you would do for wudu (3times). Putting water in your nose like you do for wudu (3times) then allowing the water to reach all parts of the body. I’m not sure about other fiqh but I think most say that these acts must be met for ghusl to be valid as well as making intention.