Camera shaking on crouching and rotating player

Hello everyone, actually I am having problem with the camera following the player. When the player moves the camera shakes and this effects more when the player is in the crouch position. I am using root motion motion for player with animations by mixamo.

My player script is like this:

 Transform cameraT;
 void Start () {
 cameraT = Camera.main.transform;
 }
 void FixedUpdate ()
     {
 float sideMotion = Input.GetAxis("SideMotion");
 float straightMotion= Input.GetAxis("StraightMotion");
 if (Mathf.Abs(sideMotion) > 0 || Mathf.Abs(straightMotion) > 0)
         {
             transform.eulerAngles = new Vector3(transform.eulerAngles.x, cameraT.eulerAngles.y);
 
         }
 }

Camera Script:

     public float distanceFromPlayer=2f;
 
     public float mouseSensitivity=6;
 
     public Transform player;
 
     public Vector2 pitchConstraint= new Vector2(-30,80);
 
     Vector3 rotationSmoothVelocity;
     Vector3 currentRotation;
     public float rotationSmoothTime = 0.2f;
 
     float yaw; //Rotation around the vertical axis is called yaw
 
     float pitch; //Rotation around the side-to-side axis is called pitch
 
     private void LateUpdate()
     {
         yaw += Input.GetAxis("Mouse X") * mouseSensitivity;
         pitch -= Input.GetAxis("Mouse Y") * mouseSensitivity;
         pitch = Mathf.Clamp(pitch, pitchConstraint.x, pitchConstraint.y);
 
         currentRotation = Vector3.SmoothDamp
             (currentRotation, new Vector3(pitch, yaw), ref rotationSmoothVelocity, rotationSmoothTime);
 
 
         transform.eulerAngles = currentRotation;
 
         transform.position = player.position - transform.forward * distanceFromPlayer;
     }
 }

For public transform I just Added an empty game object to player chest level and parented it to player. I got few of the rotating camera smoothly trick from an online tutorial, but, that exact thing won't work on player rotation though.

A character controller is attached to player without any rigid body or collider.