You have to hire a licensed electrician since it is a rental apartment. You can not add a gfci outlet off of the existing wire to the vanity light unless it is a 20 amp circuit and only powers that bathroom (I highly doubt that is the case) Since your not allowed to just leave it alone, you're basically forced to do it all to code now. A 20 amp circuit has to be ran to the panel for a GFCI receptacle. You might be able to buy a cheesy wall sconce with a switch built in but at that point you might as well add a switch (perhaps on the plate with the GFCI) and power the light that way.

intresting why the inspector told me to do it that way. I did get two wall sconces at Lowes that have switches on them..... they are a nice antique brass with a nice glass shade and weren't expensive and don't look bad at all. I have them in my place and don't mind them at all. I do like the Idea of adding in a switch next to the GFCI outlet.

I do know all the breakers are 20 amp seimens breakers in a 100 amp panel so there is a possablily it is on its own. Nothing in the panel is labled so I would have to start flipping them till the right one is found and see if that's all that is off when I find the right one.

You mentioned a 15 amp lighting circuit so make sure it is not actually 14 gauge 15 amp wiring over-fused with a 20 amp breaker. I still believe it wouldn't be wise to do much more than swapping the fixture without a licensed electrician. This is an actual requirement, not just my opinion. Things are much different when it is not your own home and other people live in it. It wouldn't hurt to go ahead and figure out what is on the same circuit.