Why am I not accelerated by the reaction force applied by earth on me?
Because the net force on your centre of mass is zero.
The upward force on your feet is of the same magnitude as the downward force of gravity.
Your major leg bones and spine are in compression because of the opposing forces.
I know that these forces will not cancel each other out since they are applied on different bodies and not a single
You are mistaken. The planet's gravity acts on your body. The reaction force from the ground also acts on your body.
masses are different
Yes your body exerts an attractive gravitational force on the planet and your feet apply an opposite repulsive force to the planet.
However if your reference frame is the planet's local surface and the planetary mass is many orders of magnitude greater than yours, you can ignore your effects on the planet as a whole.