I hit my hand on a chair, and now the area around my thumb and on my wrist is swollen and bruised and very painful.

Monitor: You could have just bruised it, depending on the force, you could have fractured it. If the swelling doesn't get better with icing I will get a n X-Ray and see a doctor.

Possible contusion: sounds like a contusion or bruise. but what might appear to be a simple force could be enough to sprain a joint or break a bone. be sure to see your doctor for an evaluation and possibly x-rays. just to be sure.