Typical hierarchy:

Player
└── Camera

Horizontal rotation usually affects the player, while vertical rotation affects the camera.

Vector2 look =
    Mouse.current.delta.ReadValue();

pitch -= look.y * sensitivity;
pitch = Mathf.Clamp(
    pitch,
    -90f,
    90f
);

transform.localRotation =
    Quaternion.Euler(
        pitch,
        0f,
        0f
    );

player.Rotate(
    Vector3.up *
    look.x *
    sensitivity
);

Lock the cursor:

Cursor.lockState = CursorLockMode.Locked;
Cursor.visible = false;