The issue was with this piece of code, now it works just perfect.

private void StateMachine()
{
    horizontalInput = Input.GetAxisRaw("Horizontal");
    verticalInput = Input.GetAxisRaw("Vertical");

    if((wallLeft || wallRight) && verticalInput > 0 && AboveGround())
    {
        if (!pm.wallrunning)
        {
            StartWallRun();
        }
    }
    else 
    {
        if (pm.wallrunning)
        {
            StopWallRun();
        }
    }
}