When I just move my hands around, how is the momentum being conserved? I guess when I'm moving my hands around, the electrostatic potential stored in the chemicals in my body is converted to motion of my arms?
But what about momentum conservation? I think the brain sends Electrical signals to my arm, which probably further use the potential energy stored in my muscles' chemicals to make my hands move.
If, at the fundamental level, electrostatic repulsion is all that's causing the movement, then the electrons in my body which apply repulsion force to my muscles (to make them move) must have gained momentum equal to my muscles in the opposite direction? Is this where the momentum goes? To the floating electrons inside my body? But still those tiny atoms inside my body, which gained this extra momentum in the opposite direction of the muscle movement, can't keep floating around in my with that extra momentum forever, right? I mean.. the body has a boundary. The atoms with this newly gained momentum will interact with the other organs, further passing on the momentum. And my body will be destined to hold this extra momentum forever?
The fact that living things can freely move their organs around around at free will really puzzles me. Can some explain living body physics to me? How can they just freely "create motion" while also adhering to physical laws like momentum conservation?
 A: 
But what about momentum conservation?

Momentum conservation doesn't apply to your body,
because your body is not an isolated system.
Your body is in contact with the ground,
and therefore there are also forces acting from your body
to the earth and vice versa.
Therefore, when you move a part of your body,
you also change the momentum of the earth.
Quoted from Momentum conservation:

In physics and chemistry, the law of conservation of momentum
(or the law of conservation of linear momentum) states that
the momentum of an isolated system remains constant.

Therefore momentum conservation applies only to whole system
(earth + your body + other bodies).
Well, this is still an approximation, because it neglects the
moon and the sun. But you get the idea.
A: In addition to Thomas' answer about the enlarged isolated system,  one  should include the infrared radiation (heat)  produced by the friction induced by the moving muscles.
One gets very hot during muscle exercises . That radiation also takes away momentum.
