oh wow, yes, I go through this same thing! I have figured out that one of the hardest parts of showering is the fact that it drowns out any outside noise so I won't know if something is happening, someone is coming into the apartment, etc. Of course I have the doors locked, I ALWAYS have the doors locked, but it doesn't take away that irrational fear.
I have been known to go a long, long time without showering for this very reason. :/
Also have the same issue with vacuuming, I need to be able to hear what is going on around me or I'm just too scared