Matthew, thanks for submitting a topic so near to my heart (erm… hands)!
So, the critical piece here is that what is commonly thought of as "left" and "right" handedness, is probably more accurately described as a spectrum. Where we lie on that spectrum (from strongly right handed, to strongly left handed) can depend on the task we are performing. For example: you might be strongly left handed when it comes to writing, but you find it more natural to open a jar with your right hand. Or when you open the lid of a hinged box, you do so with either left or right hand.
Now, I'm about as far to the right-handed side of the spectrum as a person can possibly be, although it took an epically disastrous day on my rowing team to convince my coach that I couldn’t use my left hand for rotating objects… But it sounds like you're more in the middle of the spectrum. And that's both pretty cool, and totally normal.
Folks have developed questionnaires aimed at categorizing the degree of an individual’s handedness. Turns out, there is a big range of tasks we do with our hands that demonstrate our “handedness”.
Let’s try a mini-quiz (taken from here)
Do you use always left, usually left, no preference, usually right, and always right….
… to write a letter legibly
… to throw a ball at a target
… at the top of the broom to sweep dust from the floor
… to hold a match when striking it
… to hold thread to guide through the eye of a needle
… to unscrew the lid of a jar
For an interactive questionnaire, check out this handedness survey based on the Edinburgh Handedness Inventory.
Did you know that there is such a thing as "footedness"? Just as we prefer one hand or another for certain tasks, so do we have a bias as to which foot we use. Some examples: do you always kick a soccer ball with the same foot? When you start climbing stairs, do you always lead off with the same foot? I'm a road cyclist; I use pedals that I clip into. When I unclip my shoes form the pedals, I always unclip the same foot, in the same direction.
We don't really have a good handle on what it is about the brain that makes us handed (or footed). But we do know that other animals also show similar preferences. So it's possible that handedness is some kind of fundamental feature of the way brains generate movement, and interface with muscles.
As a final note: you mentioned characteristics associated with each hemisphere. The myth of left/right brain divide, logical versus creativity, is pretty widely discredited in academic circles. It sure sounds great, which is probably why it remains such a part of our popular culture (also see: 10% myth, Lucy; coverage by NPR, Slate, or Wired – take your pick). But while there are clearly some (subtle) differences between the left and right hemisphere’s of our brain, the idea that logic and creativity are the exclusive purviews of a single hemisphere is incorrect (see: The Guardian, NPR, or NYTimes).