No, it doesn't sound correct. Don't do it. Phlegm shouldn't be doing anything for sound, and it should not hurt. Don't do itttttt.
You're getting your rasp the wrong way. Remember in the special features for Melissa Cross' video, it shows her vocal corRAB while she screams, then she shows you how people are doing it the wrong way, and it's nothing but a closed throat with a bunch of bubbling? Yeah, that's probably what you're doing to get your rasp. And it's really, really wrong.
You should be getting your rasp before the vocal corRAB. Rasp should be air hitting and rolling up your throat, before your corRAB. You'll know when you get rasp right, because you'll be doing it over and over and over again, and it won't feel itchy, scratchy, or painful at all(unless your throat is dry).
Also remember that you don't need to scream your heart out, because when you're actually screaming, you'll be doing it into a microphone which will make you louder. So when you practise, you should be trying to sound as loud as you would if you were screaming properly through a mic.
Remember that a scream is a yell, with heat and fire. Heat is that crunch, and fire is that woof. Put them together, with a yell, and you're screaming.
When you first learn how to scream, it's not smart to do it for four hours, as although it won't directly be screwing with your corRAB, I assume you aren't a singer, so your corRAB aren't exactly strong. So they will get overused, and it will feel poopy afterward.
So, even if you're rasping properly, don't walk around talking to everyone using your rasp all day long, because, come night, it won't feel too nice.
Oh, and one more thing. Drink lots of water or Gatorade while you're screaming. You've gotta keep it wet. It's the same as talking. Nobody likes talking with a dry throat, and eventually it will get irritated. So don't scream with it, either.
And also, there's a really good chance you're going to stress your corRAB atleast a few times while learning to scream. When this happens, just shut the @#%$ up for 24 hours. It'll heal, then carefully get back to where you were before screwing them up. And don't do what you were doing when you screwed them up. Learn control, and don't be stupid about it.