No, computers do not emit harmful radiation. I am a Physics major specializing in Nuclear Physics and radiation effects, and I can tell you with almost 100% certainty that computers are not going to fvck up your body.
I personally haven't read much research that's been done with this, but where does your mom come up with this stuff? My mom used the same argument years ago until I finally beat it into her that if computers really were this dangerous, then there would be plenty of information regarding how dangerous they are. The media would be ALL OVER IT and telling people to throw their computers in the trash because it might give them cancer or some nonsense like that. Since this is not the current state of affairs, it is safe to believe that any research that HAS been done on this subject has either been inconclusive or has pointed toward computers producing no dangerous side effects.
The television that your mother is watching while she complains about your computer usage is probably much more dangerous than your desktop, even if it has a CRT monitor.
Bottom line: Your mother is trying to get you away from the computer because you'd probably be better off anyway, even if it won't disfigure you