A rare disorder that causes one to cry tears of blood?

Factual Questions
1

I once heard that there is a rare disorder of the tear ducts that cause a person to cry blood. Basically, the tear ducts are constantly bleeding (resulting in an annoying crusty build up at the corners of the eyes) but it is only noticeable to others when they become irritated, such as from allergies, or crying (which results in blood tears).

Is this for real? I could only find one or two references on the Internet to some Mexican girl having this disorder. It sounds plausible, but also a little “to good” to be true. Is it?

2

Well, according to Babylon 5, this can happen if you strain yourself at telepathy.

After that, I know nothing.

3

According to James Randi, most of these cases (like stigmata - pierced wounds on hands/feet like Jesus) are just fraud. People can’t demonstrate that it happens spontaneously - only when no one is around.

Same goes for people with crying statues, walls, paintings and such.

Also, this type of stuff s disproportinately popular in Mexico and other Latino countries.