What could be causing my eye twitches and nosebleeds?

Not related. It is very unlikely your nosebleeds are caused by your eye twitching or vice versa. Eye twitches may be associate with the anxiety associated with nosebleeds. Try using saline nasal mist / saline nasal gel for the nosebleeds. If the bleeding persists, go see your doctor. Not getting better afterwards, see an ENT doctor.
Dryness. If you have dry eyes and nose then it may twitch or bleed. If well hydration by mouth, artificial tear drops and nasal saline spray does not help then please see a doc.