MrsD: sorry I didn't see this question before...it can if fact be a number of things:
Shoes: believe it or not, the wrong shoes can throw everything off-balance
Posture: best running position? Shoulders back, chest forward, arms fairly loose and relaxed (I've struggled if my arms are too tight) and head looking forward.
Core: core and posture go hand in hand, but strengthening the core makes running a lot easier.
I intentionally work on my running posture at least once a week, it really does help. Don't worry with time, practice and patience, you will notice a big difference and it really does get easier.
To get healthy mind, body and soul!