Wow, I have to say all the "advice" up here isn't all that good, though I won't point fingers.
First off, if you use your throat to scream, your gunna fuck that shit up REAL quick. You need to use your diaphragm, which if your not used to using it intentionally you have to practice muscle control for it. You also have to get into the habit of "picturing" your sound in your head, and picturing your throat like a hollow tube (trust me, it helps). The more your throat is closed off, the more you have to push to get the air out. The more you push, the more you strain your vocal chords and any spit in your throat will "gurgle" and can cause your throat to scrath and scar. As you can see, thats a BAD thing.
Avoid acidic things, like lemonade and soda. This should be self explanitory, acidic=acid acid=ow. Milk is debatable, Ive heard good things about it but I do fine without it. The few times I have used it, it just coats your throat for a few minutes and you can't tell by the feeling in your throat if your doing it right. And if your not and the coat wears off, its gunna hurt. Im not saying you shouldn't drink these things ever again, just not the days you practice by yourself or with your band, and definatly not during a show! Same goes for smoking and drinking alchohol. Im a smoker, but the day of practice I don't smoke until Im sure Im done screaming for the day.
Warm up. I know that sounds stupid, but your voice is your instrument, and you need to take care of it. Athletes can testify to warming up. Working with "cold" muscles can EASILY cause pulling muscles and other pains. You DONT want to pull the muscles in your throat, experiance can say, it fucking HURTS. Try warming up by singing, just do the "do re me fa so la te do" shit for a bit, and slowly try screaming it. You may sound ridiculous, but its just something to do to make things better. You can sing random songs, humming works in a pinch, or just going "EEEEYOW" a few times before you do it for practice can also work when your restrained for time. I usually spend about 15-20 minutes warming up, and it helps.
I suggest to just learn how to use your diaphragm to scream, NOT your throat. Look up on youtube "screaming vocal tips" and other related tags as well, and you can find alot of great help (as long as alot of shitty help). If any of them say "if it hurts your doing it right" then they are just fucking stupid. Though there IS a disclaimer for even that statement: There is a difference between pressure and pain.
You WANT pressure on your throat when your done as you just start practicing. It means your muscles are getting trained. Compare it like this: You ride a bike for the first time and you end up going quite a distance and back. Your legs feel tight. Same goes for screaming, though again make sure you pay attention to whats pain and whats pressure. Thats all I can say really.