Suppose I am walking forward and accelerating. This means the net force is forward, so some force acting on me must be pointing forward.
Aside from gravity (mg) and normal force from the ground, what forces are acting on me?
Moreover, I know that friction does not do any work on my body. Then I am doing work to myself?
You apply torques/forces with your trunk and muscles to the ground. In return, you get external ground reaction forces which moves your body.
These ground reaction forces will have both normal and tangential components on the ground. As long as these two components are in the friction cone there will be no slide so tangential components will move you forward.
