Is there any way to limit my Internet connection to a per program basis?

"You can configure apt to restrict its download speed by setting a configuration file in /etc/apt/apt.conf.d/, as detailed in this post

Specifically, create a file:

/etc/apt/apt.conf.d/76download

that contains the text:

Acquire { Queue-mode ""access""; http { Dl-Limit ""65""; }; };

where ""65"" is the speed in kb/s"