I have the same problem on my right side. only after running about a mile. I attempt to run through it and sometimes it goes and sometimes it stays as a dull pain.
My fitness instructor says its something to do with my breathing as i never used to run so much and that it will go completely when my body adjusts to the exercise that i now do.. althought im just waiting for that to happen.
I dont think it is down to age or fitness as a couple of months ago i was unfit and didnt get the pain and now im fit i get it and im only 24.
I think i will just deal with this unless it gets worse as im hoping that it will disappear and i doubt the doctor will have anything good to say other than stop running!