我流鼻血了is the best.

Generally speaking, we don't use "鼻" this single word to express nose, “鼻子” is a common expression. So you can say “我鼻子出血了” here. And also you can use the verb “流” （flow）here. the whole sentence is "我流鼻血了", it's a better one i think.

You are right 但是中国人经常用的是——我流鼻血了

我鼻子出血了；我流鼻血了

or you can say ：我鼻子流血了