Cross training won't hurt and it's recommended for runners to reduce the risk of overuse injuries while building aerobic capacity. But if your goal is to improve at distance running then you're going to have to run.

Instead of grinding out a slow 11 minute mile try running at a 9 minute pace for a shorter distance. Then rest for a few minutes and repeat several times. Do that a few times per week and gradually increase the distance you run at the 9 minute per mile pace. Eventually you'll get to a full mile at your target pace.

Also if you're overweight you're going to struggle with running and be at higher risk of injury. If that's your situation then stick to lower impact sports until you drop the extra weight, then ramp up the running.