SphereCast help

My problem is this. My player can run around a tube with no problem but when the tube makes a curve she's always looking forward like this:

The first arrow is where I want her to be looking, at the second is what she is doing because there is no rotation.

The problem starts here:

I want her to turn on the curve here looking at the tube, not always forward.

Where is my code

         Ray ray;
         RaycastHit hit;
 
         // movement code
         
         Vector3 dir = Vector3.zero;
         dir.x = Input.GetAxis("Horizontal");
         if (dir.sqrMagnitude > 1)
             dir.Normalize();
         
         dir *= Time.deltaTime;
         transform.Translate(dir * Aspeed);
         //myTransform.Rotate(0, Input.acceleration.x * turnSpeed * Time.deltaTime, 0);
         //myTransform.Rotate(0, Input.GetAxis("Horizontal") * turnSpeed * Time.deltaTime, 0);
 
         // update surface normal and isGrounded:
         ray = new Ray(myTransform.position, -myNormal); // cast ray downwards
         if (Physics.Raycast(ray, out hit))
         { // use it to update myNormal and isGrounded
             isGrounded = hit.distance <= distGround + deltaGround;
             surfaceNormal = hit.normal;
             Debug.DrawLine(transform.position, hit.point, Color.blue);
         }
         else
         {
             isGrounded = false;
             surfaceNormal = Vector3.up; // assume usual ground normal to avoid "falling forever"
         }
         myNormal = Vector3.Lerp(myNormal, surfaceNormal, lerpSpeed * Time.deltaTime);
         Vector3 myForward = Vector3.Cross(myTransform.right, myNormal); // find forward direction with new myNormal
         Quaternion targetRot = Quaternion.LookRotation(myForward, myNormal); // align character to the new myNormal while keeping the forward direction
         myTransform.rotation = Quaternion.Lerp(myTransform.rotation, targetRot, lerpSpeed * Time.deltaTime);
         anim.SetFloat("Speed", moveSpeed);
         myTransform.Translate(0, 0, 1f * moveSpeed * Time.deltaTime); // auto move the character

If I use

 myTransform.Rotate(0, Input.GetAxis("Horizontal") * turnSpeed * Time.deltaTime, 0);

she can rotate but I just want to control the player rotation around the tube, not the curve rotation.

I appreciate if someone can help me.

EDIT: If I add to my code

 if (Physics.SphereCast(transform.position, 0.5f, -transform.up, out hit, 5))
         {
             transform.rotation = Quaternion.Lerp(transform.rotation, Quaternion.LookRotation(Vector3.Cross(transform.right, hit.normal), hit.normal), Time.deltaTime * 5.0f);
         }

it does exactly what I want and align the player with the tube, but it makes the player do "small jumps" as if she were walking over spheres.

Can anyone help me avoid that?