Today I discovered one incredibly useful app that allows you to remote control your computer using your mobile phone. However, you need to be connected to the internet on both the phone and the computer and the problem is I only have a limited amount of data to use every month on my phone which would probably last me about a week if I were to use this app everyday. Is it possible to remote control a computer from far away without being connected to the Internet on the mobile phone? I really hope it is.
No, there isn't.
The internet is what allows computers to connect to each other when they are not on the same network. This would technically be possible if both devices were connected to the same network (most commonly the same router or ethernet hookup), but when your device is connected to a cellular connection, the internet it is the only way to connect your computer and phone.
No. The reason you need your limited data is because that is how the data gets transferred from one device to another. Through internet. In order to send commands (which are basically data packages) to a device, you have to have a connection with that device. That connection is internet. There are other forms of data transfer methods of course (i.e. radiowaves) however that is no use in this case.