No, you will not break the sound barrier in that scenario. The speed of sound is approximately 767 miles per hour at sea level under standard atmospheric conditions. However, it's important to note that the speed of sound is not solely dependent on the speed of the aircraft but also on other factors like temperature, altitude, and air density.
When you run forward inside the plane at 10 miles per hour, your velocity relative to the air inside the cabin would be 10 miles per hour. This velocity is relative to the aircraft, not the surrounding air outside the plane. Therefore, it does not contribute to the overall speed of the aircraft relative to the speed of sound.
Since the plane is traveling just slower than the speed of sound, and your added velocity is much smaller (10 miles per hour), the combined velocity of the plane and your running will still be below the speed of sound. As a result, you will not break the sound barrier in this situation.