Insect bites from bugs in the dog run??

I know this question isn't strictly related to dogs, but here goes... I've been bitten twice in the last week by a flying insect in our local dog run (New York City), and my ankle and face have had a lot of swelling and itching around the site of the bite. It doesn't warrant my going to the doctor >yet<, but I was wondering if any of you have been bitten like this? I hate bugs, don't know anything about them. I've seen fat green shiny flies around, could it be them? I grew up in the Mediterranean, so I don't think these are mosquito bites... any ideas as to what this insect could be? Like I said, I know this isn't a dog question, but thought I'd had more luck if I asked folks who frequent dog runs. Thanks...