Hey, stupid question - what if you're left handed? Is your right side of the brain then also on the left? I mean, are they switched?

Probably not... otherwise all these tests would be useless and they should ask you if you're lefthanded first. Or did they?
I was thinking something similar myself. I found this little snippet
"According to most experts, about 90 percent of the world's population is right-handed. Of the remaining 10 percent, about half are "strongly" left-handed. Which is to say, in about 5 percent of people, the right hemisphere is dominant and controls language.
Almost twice as many males as females are left-handed. And according to British psychologist Marian Annett, more than twice as many artists, musicians, mathematicians, and engineers are left-handed as would be expected by chance. [...] About 10 percent of left-handers suffer from language disorders and reading disabilities, while only 1 percent of right-handers do. And recent studies suggest that left-handers are three times more likely to suffer severe migraine headaches and certain types of autoimmune diseases than are right-handed people.
According to Harvard neurologist Norman Geschwind, the cause for left-handedness may lie in testosterone, the male hormone. Geschwind believes testosterone slows the growth of the left hemisphere, thus favoring greater development of the right. "Consequently, males end up right-handed less often than females."
"Understanding Human Behavior" by McConnel, James V, p39.
I'm right handed but my left thumb rests on my right thumb when I clasp my hands. Although there are differences in the structure of both sexes brain I think they are both capable of doing each others job. And as for dominance I'm not convinced that overall there is a dominant hemisphere. Each hemisphere may be dominant in a certain area but how do you quantify what one is in charge? Doing a lot image streaming at the moment and it's all team work I can tell you!
I'm Bigger, and Bolder, and Rougher and Tougher, in other words Sucker, there is no other...no other...I'm bigger, and bolder, and rougher in other words sucker there is no other,I'm the one and only Dominator, I'm the one and only Dominator
Wanna Kiss Myself
Human Resource Had to get that out my head.
If you're interested in that, I'm sure you've read the book "The curious incident of the dog in the night time"?
I've heard of it but never read it. I'll add it to my list!