Orbiting Player With Camera

I'm trying to make a third person shooter at the moment, and I've run across a bit of a snag when looking for the right camera script.
I found something good for a first person viewpoint, but it doesn't work for a third person game because when it rotates vertically it won't pivot around the character (on the Y axis) as I'd like it to.
I'm basically looking for something like the camera in fortnite, tbh.
The X axis works perfectly, and it'd be great if anyone knew how to integrate a functional orbit for the Y axis too.
I attached a file with a pic I drew basically outlining what I need it to do lol.
Thanks in advance!

Code (CSharp):

1. using System.Collections;
2. using System.Collections.Generic;
3. using UnityEngine;
4.  
5. public class AlternateMouseLook : MonoBehaviour {
6.     public enum RotationAxes { MouseXAndY = 0, MouseX = 1, MouseY = 2 }
7.     public RotationAxes axes = RotationAxes.MouseXAndY;
8.     public float sensitivityX = 15F;
9.     public float sensitivityY = 15F;
10.  
11.     public float minimumX = -360F;
12.     public float maximumX = 360F;
13.  
14.     public float minimumY = -60F;
15.     public float maximumY = 60F;
16.  
17.     float rotationY = 0F;
18.  
19.    
20.  
21.  
22.  
23.     // Use this for initialization
24.     void Start () {
25.        
26.     }
27.  
28.     void Update()
29.     {
30.         /*
31.         if (axes == RotationAxes.MouseXAndY)
32.         {
33.             float rotationX = transform.localEulerAngles.y + Input.GetAxis("Mouse X") * sensitivityX;
34.  
35.             rotationY += Input.GetAxis("Mouse Y") * sensitivityY;
36.             rotationY = Mathf.Clamp (rotationY, minimumY, maximumY);
37.  
38.             transform.localEulerAngles = new Vector3(-rotationY, rotationX, 0);
39.         }
40.         else if (axes == RotationAxes.MouseX)
41.         {
42.             transform.Rotate(0, Input.GetAxis("Mouse X") * sensitivityX, 0);
43.         }
44.         else
45.         {
46.             rotationY += Input.GetAxis("Mouse Y") * sensitivityY;
47.             rotationY = Mathf.Clamp (rotationY, minimumY, maximumY);
48.  
49.             transform.localEulerAngles = new Vector3(-rotationY, transform.localEulerAngles.y, 0);
50.         }
51.         */
52.    
53.         if (Screen.lockCursor == true)
54.         {
55.             if (axes == RotationAxes.MouseXAndY)
56.             {
57.                 float rotationX = new float();
58.  
59.                 if (transform.parent != null && transform.parent.CompareTag("Player") == true)
60.                 {
61.                     rotationX = transform.parent.transform.localEulerAngles.y + Input.GetAxis("Mouse X") * sensitivityX;
62.  
63.                     rotationY += Input.GetAxis("Mouse Y") * sensitivityY;
64.                     rotationY = Mathf.Clamp(rotationY, minimumY, maximumY);
65.  
66.                     transform.parent.transform.localEulerAngles = new Vector3(0, rotationX, 0);
67.                     transform.localEulerAngles = new Vector3(-rotationY, 0, 0);
68.  
69.                 }
70.                 else if (transform.parent != null)
71.                 {
72.                     rotationX = transform.parent.transform.localEulerAngles.y + Input.GetAxis("Mouse X") * sensitivityX;
73.  
74.                     rotationY += Input.GetAxis("Mouse Y") * sensitivityY;
75.                     rotationY = Mathf.Clamp(rotationY, minimumY, maximumY);
76.  
77.                     transform.parent.transform.localEulerAngles = new Vector3(0, rotationX, 0);
78.                     transform.localEulerAngles = new Vector3(-rotationY, 0, 0);
79.                 }
80.                 /*
81.                 else {
82.                     rotationX = transform.localEulerAngles.y + Input.GetAxis("Mouse X") * sensitivityX;
83.  
84.                     rotationY += Input.GetAxis("Mouse Y") * sensitivityY;
85.                     rotationY = Mathf.Clamp (rotationY, minimumY, maximumY);
86.  
87.                     transform.localEulerAngles = new Vector3(-rotationY, rotationX, 0);
88.                 }
89.                 */
90.             }
91.             else if (axes == RotationAxes.MouseX)
92.             {
93.                 if (transform.parent != null)
94.                 {
95.                     transform.parent.Rotate(0, Input.GetAxis("Mouse X") * sensitivityX, 0);
96.                 }
97.                 else
98.                 {
99.                     transform.Rotate(0, Input.GetAxis("Mouse X") * sensitivityX, 0);
100.                 }
101.             }
102.             else
103.             {
104.                 rotationY += Input.GetAxis("Mouse Y") * sensitivityY;
105.                 rotationY = Mathf.Clamp(rotationY, minimumY, maximumY);
106.  
107.                 transform.localEulerAngles = new Vector3(-rotationY, transform.localEulerAngles.y, 0);
108.             }
109.         }
110.     }
111.  
112.    
113. }
114.  

 

Look at Unity Cinemachine. Should solve your concerns.