It's probably normal. Lots of little kids go through a phase of acting out physically, especially when they haven't learned enough words to communicate their frustration easily. My 2-year-old, Liam, is going through this now.
There are some things you can do to help your son get through this phase more quickly -- and help you survive it:
React quickly and firmly. Immediately say "No biting" in a calm, stern voice. Take him to a quiet place where he can calm down.
Be consistent. I know it's hard, but if you let him bite sometimes because you're too worn out to deal with it, he assumes that biting is okay -- and will continue.
If he's just screaming, ignore him. Show him that's not the way to get your attention.
Give positive feedback for stopping. If he manages to calm himself down, let him know how proud you are of him.
Watch for triggers. Does he get out of control more often when he's tired? Hungry? (Both are true for Liam.) If so, try to make sure he gets enough sleep and eats regularly. And try to plan around his most difficult times. If late afternoons are impossible, for instance, don't run errands or make play-dates then.
Distract him. This is one of the key survival strategies for toddlerhood. When he starts working himself up, quickly step in with something that's a favorite, or just unexpected ("Hey! Let's do the Chicken Dance!"). You'll be amazed how often it works.