Managed to solve it. A quick tutorial to how to do it:

Create a Empty GameObject and a Cube, and stretch the cube to make the arm. Make the Empty GameObject be the parent of the Cube. Make sure that the Empty GameObject is in the end of the cube. It should be on the "sholder" of the "arm".

Add the following code to the Empty GameObject. It's a modification of the MouseLook.cs:

// using UnityEngine; using System.Collections;

public class MouseLook : MonoBehaviour { public float sensitivityY = 15F;

public float minimumY = -60F;
public float maximumY = 60F;

float rotationY = 0F;

Quaternion originalRotation;

void Update ()
{
    rotationY += Input.GetAxis("Mouse Y") * sensitivityY;

    rotationY = ClampAngle (rotationY, minimumY, maximumY);

    Quaternion yQuaternion = Quaternion.AngleAxis (rotationY, Vector3.left);

    transform.localRotation = originalRotation * yQuaternion;
}

void Start ()
{
    if (rigidbody)
        rigidbody.freezeRotation = true;
    originalRotation = transform.localRotation;
}

public static float ClampAngle (float angle, float min, float max)
{
    if (angle < -360F)
        angle += 360F;
    if (angle > 360F)
        angle -= 360F;
    return Mathf.Clamp (angle, min, max);
}

} //

It may have some unnecessary lines of code. I didn't filtered what I need, only modified to follow the mouse in 2D.

The "arm" - the stretched Cube - will point to the mouse, because the Empty GameObject is always facing the mouse position.

Hope that it helps somebody.

I have actually used this in my 2d game but I had to completely scrap the X axis part of the code. It worked perfectly then.