The Externalexternal IP Addressaddress is assigned by your ISP to your router which in turn assigns different Internalinternal IP Addressesaddresses to all devices in the network. The outside world can only see your external IP address. In short, it cannot distinguish between your dad's computer and yours.
When a Serverserver sends you some data, it will be transmitted only to your device by your router (because you requested it) and not your dad's. (pleasePlease correct me if i'mI'm wrong.)