If you're screaming, just be sure not to try and limit the scream by closing your vocal cords. You'll hurt your self if you do. Always, always, always push from your diaphragm, and always keep the tip of your tongue at the bottom teeth(for vowel sounds). Any tension in your neck or throat can hurt you, and it's a sign that you're singing incorrectly. Sing with you head at a comfortable position. If you move your head down to hit low notes, or stretch to hit high notes, that's bad.
If you can afford it, I highly recommend Roger Kain's Complete Vocal Workout, and a vocal coach if you can find one. The former is a series of exercises for modern vocalists taught by an opera singer. It works. My vocal coach is blown away by how strong I've gotten in the past 2 weeks. The progress is due to, in no small way, the exercises in the book.
Your low range is probably due to you not knowing how to sing properly. Generally, a baritone should be able to sing tenor parts if they're trained correctly, and vice versa. It's a lot of work to get your mixed voice and head voice strong. Chest voice is easier for most people, but it's still a lot of work.
If nothing else, get one of the Kain books. He has 2 or 3 out. Also, if you need help with specifics, don't hesitate to ask here. If you ever have pain in your throat/vocal cords, stop what you're doing. Ideally, a coach is going to be the best bet. You'll have someone there to listen to and watch what you're doing. You'll get good feedback on what you're doing wrong and what you're doing correctly. I tape each session with my coach, and it's quite helpful in remembering exercises she teaches, and to hear what I sound like, both good and bad. I recommend it, as painful to the ego as it is.
