Don't quite agree with the medical advice below. Have always been told to pinch the nose closed or mostly closed until clotting occurs (Mayo Clinic allegedly agrees: http://www.mayoclinic.com/health/first-aid-nosebleeds/HQ00105) and apply a moderate cold pack to slow blood flow if possible. Don't pick, and don't blow if you can avoid it, until a while after it stops bleeding. If it bleeds again, then you can blow out the old clots that didn't stick to the nasal lining, to keep them from going somewhere else; but don't pick, do pinch the nose closed again, and get right to a doctor if it doesn't stop within a reasonable period. And if you snort any illegal substances, I guess you'd better stop. Yecch.
And while "blood thinners" or oxygen through cannulas can trigger nosebleeds, I've never heard any evidence that emotional issues can cause them.
Anyway, this is a good ep about guilt and loyalty, choosing which people to trust, and the conniving of a guy with a grudge, delusions of grandeur, and narcissistic personality disorder. And a reminder that hospitals can be very scary places if you know what's up.
Try to avoid ever checking into a hospital without an advocate you know well to watch your back. A lot of mistakes DO happen in hospitals; don't be a statistic.
For the reviewer a couple entries down who doesn't know the "former detective" background: Mr. Monk was taken off the force for psych reasons after Trudy died, and at some point in this series, is offered his badge back--but subsequently, decides it's too dangerous to be on the front lines. But in this episode, he was in danger, even though he was just acting as a consultant.