You searched for: “epistaxiophobia
epistaxiophobia (s) (noun) (no plural)
The dread of a nosebleed: Ever since Sandy was a toddler and noticed red liquid coming out from one of her nostrils, she was abnormally worried and concerned about dying and, as a consequence, suffered from epistaxiophobia.

Symptoms of having this problem, or seeing someone with it, may result in a lowering of blood pressure, a reduction of one's breathing rate, and a feeling of weakness or even a fainting spell.