Estrogen is part of the problem, but by no means the whole picture. Many men have higher estrogen levels with no problems, and men have seemingly low estrogen levels and develop gyno. There are a number of other substances that are to blame as well, plus the fact that doctors don't entirely know why some men develop it.
A simple hormone test can indicate that your estrogen levels are higher than normal (if you have a previous test to compare to) but that won't really solve much. However, it's still a good idea to talk to your doctor about it. finasteride may be to blame, but it's quite rare to develop gyno from 1mg finasteride. I recall from a study that it occurred in somewhere around 0.3% of patients. However, this may only mean 'true' gyno, with an actual gland growing.
Are you sure you haven't gained any weight since starting? I believe that even if it isn't true gyno, a raise in estrogen from taking finasteride may cause your body to store more fat in your chest area, rather than elsewhere. This would likely not be permanent, since losing weight would likely get rid of this.
If you're already quite thin, on the lower end of the BMI scale, I would be suspicious that finasteride might be causing it. If its actual gland growing, there are supplements you can try (Enden can recommend those). If it's fat, lypo would definitely solve it.
It all depends on how much it's bothering you. If you and your doctor suspect finasteride might be the cause, you have to decide if it's worth continuing the medication or not.
If my story helps, when I started on finasteride I was maybe 30 pounds overweight (210 lbs). I had some gyno then due to the excess fat. I have since lost 20 pounds (plus gained muscle, so probably lost more than 30 pounds of fat) and the gyno has almost completely gone away. That was 7 months ago.