In my bathroom near the sink is a GFCI outlet. I installed a new medicine cabinet and I want to add lights that currently do not exist. I will connect these fixtures with Romex wiring that I will install. But what I want to know is, can I pigtail my new lights from the power that currently connects the GFCI on the same wall? I just read that a GFCI has to be powered by a separate circuit on another forum. But I'm not sure if this is correct. If this is the case and I CANNOT pigtail from the GFCI can I run a Romex from an outlet from the bedroom next door and run it to the same junction box. To keep things looking neat and tidy I want to replace the existing GFCI with a two gang junction box that will allow me to have a GFCI and a light switch all under one switch plate.
If I can do any of the above would you be willing to provide me with detailed instructions?
By the way, this is the light switch I want to add in the long run:
Photo of blue junction box below added 03/19/18 at 2:35PM PST
Drawing of my junction box to explain what's what:
This wiring diagram belongs to do-it-yourself-help.com. The original can be found here: https://www.do-it-yourself-help.com/gfci_wiring_diagrams.html