Just did a 3 mile run today on the treadmill.

A question for all you runners out there - I'm left-side dominant and notice when I run on the treadmill, my left leg does all the work and is always sore when I finish, my other leg is just fine. I posted this question on a running website, and was told it's very common to have a "power" side and a "skill" side and that physical therapy could help me with this issue. However, I think it will be all but impossible to get a referral to physical therapy for something related to sports activity, when my leg doesn't bother me any other time. Any ideas?