Cut open a peach and let us know what you see inside. The three primary causes of oozing on peach are oriental fruit moth, plum curculio, and environmental damage (the peach grew funny). Most likely you have OFM since it oozes the most, PC barely oozes. Environmental damage usually strikes only a few fruits. If you have OFM there will be an open hole where the ooze is coming out and a trail through the peach that is open. If its PC there will be very little ooze and the trail in the peach will look like a black line, not an open trail.

Scott