Wait a minute - are you saying you're running a 7-8 minute mile?  That is pretty fast, especially for a beginner who just started running after having been sedentary.   Maybe you need to SLOWWW down for most of your run.  (My chest would probably hurt too if I ran that fast for 30 minutes!)  The object isn't to kill yourself, the idea is to run at a pace you can comfortably maintain for 30+ minutes.  I think if you slow it down to more like a 9-10 minute mile (about 6 - 6.5 mph) you will be able to keep going longer without hurting yourself.

One of the tests for guaging whether you're running at a reasonable pace is to see if you can hold a conversation as you're running.  It doesn't have to be a lot of talking, but at the right pace you can speak a bit at intervals without wheezing and feeling like you want to fall over.  Many of the runners of my tribe (barefoot and minimalist shoe runners) drive other foks nuts by being so chatty during races.  If you run within your "groove" you're also benefitting from the right kind of fat metabolization, of which you can feel free to look up the details yourself,

Good  Luck and have fun at whatever pace you find works for you.