I literally just now noticed this, but my right eye, on the white part (whatever its called) is starting to bleed or something, the red line I normally can only faintly see, if I'm looking up close have now not only grown larger and more visible, but are starting to mix together and slowly turning the white part of my eye red. Is this some normal occurrence?

Yes, probably -- unless you have suffered an injury to your eye. Extreme fatigue that results in rubbing your eyes a lot and too much caffeine may cause a bloodshot eye. (Hmmmmmmmmmm... ) Of course, drinking to excess will cause this too. If your eyes ache, press a warm wet washcloth to them five to ten minutes at a time several times a day. If you're actually in pain, call the doctor.