@mohanr63926589 - Your computer is likely connected to a router at your home or place of business, and that router assigns your computer a local IP address. This might be something in the range of 192.168.1.x, or possibly 10.0.0.x, or something similar. This IP address is specific to your internal network (at home or work). There are likely thousands (millions? more?) of other devices around the world with the same internal IP address as you.
Your router, on the other hand, ultimately connects to the broader internet, so it requires an external IP address that is unique. No two connected devices on the broader internet should have the same IP address. For example, the external IP addresses for your home and work networks is guaranteed to be be different.
With that in mind, there is no use or benefit in trying to whitelist an internal IP address for external use.
On the specific topic of Charles Proxy and mapping a mobile device to pass data through your computer, what you need to do is set the local IP of your computer as the proxy in your mobile device's network settings. (Both devices must be on the same network.) The Charles Proxy website walks through this setup here for an iPhone, but the process is similar for most devices (Android...).
