I've had up close and personal encounters with bobcat, lynx and cougar, but never heard the cougar scream up close. The former two will certainly wake you with a start and "ungodly" is about the best descriptor I can think of. There are healthy populations of lynx higher up in the catskills but probably not near you unless they are hurt/sick or otherwise impaired. My money would be on bobcat, which are very unlikely to bother you.