Sensible advice from James, and good that you're enjoying the running. My guess would be tightness, I had the same when I restarted running a few years ago. I didn't believe that such pain could be caused simply by tight calves, but a good stretching plan should make things easier. If you're able to find a reasonable local sports massage then that will loosen things up as well.
As you build up your running, you should also think about your running shoes, what are you running in at the moment? The plan you're following sounds sensible, if you havent already discovered the Couchto5k plans then they're really good and similar to what you're doing.
To give you extra motivation have a look for your local Parkrun. They're free 5k volunteer based runs on a Saturday morning, very friendly and it doesn't matter if you have to walk part of them.