the muscle that runs down the outside/front of your shin is the muscle that lifts your foot.
running with a heel-strike loads this muscle with a shock-load with every foot-fall.
this can cause it to hurt a bit.
i find a shin-specific warm-up helps this muscle. do some toe extensions/raises, that sort of thing.
if you're new to this running lark, don't worry about trying to run for days on end, 15 to 25 minutes a couple of times a week should be enough for now. your body will tell you when it's ready to go further/faster.
you'll be half-way round your local 4k loop, and at the point where you always turn left to head home, your legs WILL just say 'nope, sorry, we're going this way' and they'll turn right, and take the long way home.