Just out of curiousity, how do you know the dreams start at 3;13? Most dreaming occurs in the REM (rapid eye movement) stage of sleep so you've most likely been asleep for upwards of 90 mins so obviously you can't be watching your clock. I was just wondering.
I also have frequent nightmares. Most nightmares are caused by our own minds, expressing fear we'd rather avoid. Your brain uses sleep to practice movement patterns without actually using the muscles. Horrific dreams often act as practice runs for our fight-or-flight mechanism. In other words, it's not something to work yourself up about and it makes total sense that your dream is specific to you and shows you familiar numbers.
However, if you're still worried, there are plenty of protection/anti-nightmare spells and meditataions on this site. It makes psychological sense that you're scared of death so it's more likely to just be a scary dream than anything latching on to you. Better to be safe than sorry though.