Unless you are willing to hire an electrician to clean up your mess, you
don't want to get involved in running a new cable. Those with 20 years of
experience forget how difficult it is.
However, you might have a very easy fix.
Find that junction box everyone was talking about. It probably has 4 cables
going to it; one to the breaker box, one to the switch, one to the outlet,
and one to the lights. The black from the breaker will be connected to the
black going to the switch. The white from the switch will be connected to
the black going to the blacks going to the light and the outlet. Does that
By moving the outlet black from after the switch to before the switch, it
will always be hot.
I think you have about a 50% chance of finding it like that. Good luck.