A few years ago I was shot in the thumb by a bb gun and the bb is still in there. You can physically see where the bb is since there is a bump and you can still see the scar about a half of a inch away. I'm not sure which type of metal it is made of I think it was copper. I'm just concerned on if they will let me fly or if it won't even be picked up. If it does will it help to have a doctors note? Or will that be no difference at all.
It's very unlikely to set off the metal detectors. Think about how many people walk through wearing eyeglasses, or in the good old days, shoes (which often contain small metal pieces).
If it does set off the detector, do not panic. Just tell them you have this thing, they can touch your finger, and they will probably wave their metal-detector wand around your hand then let you go.
A doctor's note would be useful if none of the above works out, but most likely you'll never use it. If you're going to spend the time and money to get such a note, better just spend a bit more and get the BB removed.