How to limit the angle of a camera with transform.RotateAround?

Okay, I've spent legitimately 3 days on this and I've become stumped by the 'transform.RotateAround' instruction. I'm trying to make a third person camera and it's all working fine except I can't figure out how to limit the Y Axis, so that it will stop if it gets too high or low around the character. Instead, what's happening now is if I move the camera too far it'll bug out at the 'poles' of the Y Axis.

 public class ThirdPersonCamera : MonoBehaviour
  {
      [SerializeField]
      private float distanceH;
      [SerializeField]
      private float distanceV;
      [SerializeField]
      private float smooth;
      [SerializeField]
      private Transform follow;
      [SerializeField]
      private float camSmoothDampTime = 0.1f;
      [Range (0f, 4f)][SerializeField]
      public float mouseSensitivityX = 1f;
      [Range(0f, 4f)][SerializeField]
      public float mouseSensitivityY = 1f;
  
      private Vector3 lookDir;
      private Vector3 restPosition;
      private Vector3 velocityCamSmooth = Vector3.zero;
  
      void Start()
      {
          follow = GameObject.FindWithTag("CameraTarget").transform;
      }
  
      void Update()
      {
          //Control with joystick
          transform.RotateAround(follow.transform.position, follow.up, mouseSensitivityX * Input.GetAxis("Joy X") * Time.deltaTime * 100);
          transform.RotateAround(follow.transform.position, follow.right, mouseSensitivityY * Input.GetAxis("Joy Y") * Time.deltaTime * 100);
  
          //Control with mouse
          transform.RotateAround(follow.transform.position, follow.up, mouseSensitivityX * Input.GetAxis("Mouse X") * Time.deltaTime * 100);
          transform.RotateAround(follow.transform.position, follow.right, mouseSensitivityY * Input.GetAxis("Mouse Y") * Time.deltaTime * 100);
      }
  
      void LateUpdate()
      {
          Vector3 characterOffset = follow.position;
  
          lookDir = characterOffset - this.transform.position;
          lookDir.Normalize();
  
          restPosition = characterOffset * distanceV - lookDir * distanceH;
          smoothPosition(this.transform.position, restPosition);
          transform.LookAt(follow);
      }
  
      void smoothPosition(Vector3 fromPos, Vector3 toPos)
      {
          this.transform.position = Vector3.SmoothDamp(fromPos, toPos, ref velocityCamSmooth, camSmoothDampTime);
      }
  }

This is what i have so far. Void Update is where the user controls are. I hope the internet can help. Thank you in advance!