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Add a flag to determine if the player has been stopped. At that point, stop setting the players position to the camera's, and instead some other input.

public float speed;
public test testing;
bool stopped = false;
// Use this for initialization
void Start () {
    speed = 10f;
    testing = Camera.main.GetComponent<test>();
}

// Update is called once per frame
void FixedUpdate () {
    if (!stopped)
    {
        Vector3 p = Camera.main.ViewportToWorldPoint(new Vector3(0.5F, 0.5F, Camera.main.nearClipPlane));
        transform.position = new Vector3(p.x, p.y, -1);
    }

    else
    {
        //move away here
    }
}

void OnCollisionEnter2D(Collision2D col) {
    stopped = true;
    testing.speed = 0;
    
}
void OnCollisionExit2D(Collision2D col) {
    stopped = false;
    testing.speed = 10f;
}

###Edit

Seeing how you move the camera, in your camera script I would have two different speeds

public float speedX;
public float speedY;
public float translationY;
public float translationX;
// Use this for initialization
void Start () {
    speedX = 10F;
    speedY = 10F;
}

void FixedUpdate () {
     translationY = Input.GetAxis("Vertical") * speedX * Time.deltaTime;
     translationX = Input.GetAxis("Horizontal") * speedY * Time.deltaTime;
    
    transform.Translate(translationX, translationY, 0);
}

Then you can omit the flag I talked about previously, and only modify speedY so the player can still move to the side.

public float speed;
public test testing;
// Use this for initialization
void Start () {
    speed = 10F;
    testing = Camera.main.GetComponent<test>();
}

// Update is called once per frame
void FixedUpdate () {
    Vector3 p = Camera.main.ViewportToWorldPoint(new Vector3(0.5F, 0.5F, Camera.main.nearClipPlane));
    transform.position = new Vector3(p.x, p.y, -1);
}

void OnCollisionEnter2D(Collision2D col) {
    testing.speedY = 0;
    
}
void OnCollisionExit2D(Collision2D col) {
    testing.speedY = 10F;
    
}

###Edit 2

Using this SO question we can determine where the collision was. We can then modify our code to be

void OnCollisionEnter2D(Collision2D col) {
    transform relativePosition = transform.InverseTransformPoint(collision.contacts);
    if (abs(relativePosition.x) > abs(relativePosition.y))
        testing.speedX = 0;
    else
        testing.speedY = 0;
}

void OnCollisionExit2D(Collision2D col) {
    testing.speedY = 10F;
    testing.speedX = 10F;
}