2.5D Game: How to move main Character in X & Y Axis with ability to rotate?

Hi All!

Just started with Unity. After going through couple of Tutorials, I was able to kickstart by first project. I am trying a 2.5D game , where my 3D modeled character has the ability to fly around in X (Horizontal) and Y Axis (Vertical). I was able to write the code to move him around and do bit of rotation too, so that it looks like he is flying in the given axis. (Fly function is below)

So this works fine when I don't alter the character's rotation. However, when I try his other animations where I want the model to rotate in any axis, the character starts rotating in that direction. How do I keep my char fixed to Horizontal movement, while still being able to rotate the model for certain animations(like Boost Left/Right/Up/Down)

 void Fly()
     {
         Quaternion rot=transform.rotation;
         float z = rot.eulerAngles.z, y = rot.eulerAngles.y;
 
 
         if (Mathf.Abs (horizontalInput) > inputDelay) {
             //ROTATE AROUND
 
             anim.SetInteger ("State", 1);
             z += horizontalInput * rotateVel * Time.deltaTime;
             rot = Quaternion.Euler (0, y, z);
             transform.rotation = rot;
         } 
         if (Mathf.Abs (verticalInput) > inputDelay) {
             //rotate left and right
             Vector3 pos=transform.position;
             Vector3 velocity=   new Vector3(0,  verticalInput * forwardVel , 0);
             anim.SetInteger ("State", 1);
 
             pos = rot * velocity;
             rb.velocity = pos ;
     
 
         }
         else 
         {
             //zero velocity
             rb.velocity=Vector3.zero;
             anim.SetInteger ("State", 0);
         }
     }