First, losing weight will likely help improve your times a lot. A rough rule of thumb is 2 seconds per pound per mile raced. So, dropping 10 lbs could yield around 10 lbs x 2 seconds x 3.1 miles = around 1 minute faster.
You can go to many gyms and get your body composition tested with calipers (measures your skin folds at various points on your body). This shouldn't cost much, if any to do, and is pretty accurate. Most gyms will also have some device that measures something like electrical impedance or some such... I'm not sure how accurate this is, but would likely get you in the ballpark. I believe one of the most accurate is to actually get weighed in water... but you have to find a place that does it, and it might cost you some cash.... probably not worth it for your situation when the other methods will get you in the right ballpark.
Oh, and if your goal is to run faster, losing any excess/unneeded muscle will also improve your times.