I have a hard red bump on the end of my nose.

Hard to tell: Without actually seeing it, it would be hard to diagnose what this would be. Differential at your age includes a zit, basal cell carcinoma, squamous cell carcinoma, actinic keratosis, and many others. I would recommend you see your local dermatologist to better evaluate it.

Consider a skin cancer: If the bump has been there for quite a while and is growing I would be more concerned. If it sometimes bleeds I would be concerned. This is something that would be worthwhile going to see your doctor. If it is a skin cancer you need to get it taken care of fairly quickly