Please forgive me for being so blunt here, but are your parents that naive about cats. Their cat is only 8 years old for pete's sake. That is NOT considered old.
No matter what age my cat was, if it had these symptons, it would be at the emergency vets lickety split. Since you say that it seems to hurt her when you touch her chest, did you ever think that maybe, just maybe, she might have been clipped by a car and has internal injuries, especially if she is bleeding by the nose.

I pray that your parents realize before it's too late, to bring her to a vet ASAP!!!