La llarona, good grief! That's a Texas/Mexico border tall tale that goes back to (at least) the 1800's. Now she's followed you to SC?
I've heard cougars scream and they do sound like women screaming. I don't think that's what you heard. They are SO loud that if it was in your neighborhood, your "fight or flight" would have taken over and you would be long gone. A mile away and they sound like your ordinary woman screaming for her life; but then, you can tell it's a long way off. I've also heard plenty of rabbit distress noises, but they sound (to me, anyway) more like small kid screams or babies crying.
I'm going with an owl. Like others have suggested, probably Barred or Screech. An amazing variety of vocalizations from owl. So the owl screeches and the noise in the bush is a rabbit or neighborhood cat jumping into the bush for cover.
Quick story: My friends and I used to go camping all the time when I was in high school. A favorite area was Colorado river bottom. One time a nearby woods was filled with maniacal laughter. And by that, I mean a bunch of off-the-charts crazy, nut house escapees, laughing up their freedom and future evil plans (or maybe escaped monkey radiation experiments). We were always well armed and we could tell it was animal, so we were only creeped out and not scared. The next day a neighbor farmer told us "them are rain crows makin that noise". We never heard of rain crows, so a little investigation found that was another name for Barred Owls.
lukus
*edit* Now I've googled "rain crow" because I was thinking about that time. Turns out rain crows are another name for cuckoos. These weren't yellow-billed cuckoos, I'm familiar with them too. Our investigation at the time was talking to the neighbors and granddads. I'm sure we got a "pfft, he means barred owls, not rain crows" answer. I've heard them make this same noise since, just one or two though, not a whole woods full of them like the first time.