The wireless stick in your room is just picking up the signal sent out through the netgear router that you have.
You can connect the PS3 wirelessly to the same signal if you know your wirleless network name and password. Connecting the PS3 to your netgear router won't affect your computer at all.
Here's an analogy for you. If you plug a lamp into one outlet in your home, it doesn't really affect the radio you have plugged in in another room. They're connected to the same source, but they don't really interact.
Here's a good site to walk you through the setup of the PS3. It's got screenshots for how to set up a wireless, or wired connection:
http://chasms.com/ps3/ps3.htm