Avid runners, am I the only one with this problem?

Lately I've been working on increasing my speed as well as my distance in my run. But pretty recently, every time I run, right around the first mile mark I get a very intense urge to pee. But when I pause the treadmill to go to the bathroom, little to nothing comes out. The feeling stays through the rest of my run, and goes away only after im fully cooled down and my heart rate is normal. I don't believe its a bladder infection. I've had those before, and the urge was constant, not only present during and shortly after a run.
Is this something all runners experience or should I see a doctor?
Avid runners, am I the only one with this problem?
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