Lighting, Light Fixtures, Ceiling and Exhaust Fans - I'm so confused...

I am readying up the babies room, and am installing a ceiling light. There is one switch at the doorway that controls the top outlet on one of the receptacles. I have realized that the white wire connected to the switch is hot and that when i flick the switch to "on" the black wire also becomes hot. Now I purchased a double switch and replaced the single one. Top switch control the receptacle and i want the bottom switch to control the ceiling light. This is where i get confused even with 2 books i have.
I maybe should have left the tab in but i can pigtail the hotwire to both switches. Where exactly does light fixtures wires fall into this situation. Seems to me that the white wire on the lighting fixture has nowhere to go.

You can't do it with out changing the cable between the switch and the receptacle. There is no neutral wire in the switch box.
There are 2 things you can do.
Make the receptacle always hot and use the switch for your new light.
Leave the receptacle switched and also switch the new light at the same time.

There is another receptacle on an opposing wall that I believe i could connect off of. It seems to be 2 black wires on one side and 2 white wires on the other side. I could use that perhaps?

Edit: Actual sounds easier to make that receptacle always hot and use the existing switch to control my light.

You can make the receptacle always hot merely by connecting all wires of the same color at the receptacle (all blacks to brass, and all whites to silver). Because the receptacle currently has a tab broken off, I suggest you buy a new receptacle that still has the tab intact.

Then you can just use the old single switch you took out and connect it in the normal manner (two white wires to each other, two black wires to the two screws on the switch).

Thanx for your kind help. I hate not being able to figure this stuff out but you've helped greatly. :)