I think it's totally normal, since no one is perfectly symmetrical. I've noticed this time around (I've been a runner on and off for a few years, mostly off) that sometimes my left knee aches a little and my right doesn't, and sometimes my right shin hurts and my left doesn't.
Like people have already said, intervals are a great way to build running endurance! I always listen to music while running, so a few weeks ago when I re-started, I would run for one song, walk for 2, run for 1, walk for 2... on and on for 30 minutes or so. sure, all songs are different lengths, but I figured it all averaged out, and I didn't have to wear a watch!

I worked up to walking 1 and running 1, then walking 1 and running 2... now I'm at a point where I just run most of the time and take little walking breaks when I really need to. I realize I advanced kinda fast in just a few weeks, but I just figure my body never
completely forgot how to run efficiently.
