I am sorry to say it, but nosebleeds in pets are often caused by serious conditions.
Unfortunately, your sister is correct to worry about the presence of a nasal tumor. They are a leading cause of bloody noses in older pets (8 years of age isn’t that old, but Snooky is still at risk). However, nasal tumors often are accompanied by wheezing and weight loss, and there are other causes of bloody noses. So it is by no means a foregone conclusion that a tumor is present.
Other causes of bloody noses include trauma, dental disease, foreign objects lodged in the nose (which is more likely in cats that have access to outdoor areas such as parks), and blood clotting disorders. Allergies usually do not cause nosebleeds.
Snooky definitely needs to see a vet. However, I should warn you that getting to the bottom of the problem may be difficult. Diagnosing chronic bloody noses may require blood tests as well as anesthesia for a thorough oral exam, X-rays and rhinoscopy (a procedure in which an instrument is used to visualize the inside of the nose and sinuses). Some cases require CT scans.
I wish I could offer better news. I hope, for Snooky’s sake, that the problem is easy to uncover and treat.