Object Rotating On Z Axis No Matter What

Hi,

I have an empty object in the middle of my scene and the maincamera is a child of it, offset to the side. When I rotate the empty object, the camera will look around my scene. Easy! ... no!

 public float RotationSpeed = 15;
 
     // Use this for initialization
     void Start () {
     
     }
     
     // Update is called once per frame
     void Update () {
 
         transform.Rotate((Input.GetAxis("Mouse Y") * RotationSpeed * Time.deltaTime), (Input.GetAxis("Mouse X") * RotationSpeed * Time.deltaTime), 0, Space.World);
     
     }
 }

So the only axis I want to rotate on are X and Y. I want to be able to look side to side, up and down, using my mouse. I set the Z axis to 0.

I tested it, and it worked fine except that my camera was rotating on the Z axis. I tried changing Space.World to Space.Self (I'm very new, just trying anything really) and it stayed the same.

I added a rigidbody and put a constraint on Z's rotation, still the same.

Can anyone help me figure this out? Thanks.