Is a broken ankle swollen or painful?

Yes. Fractured (broken) ankles can be both painful and swollen. There are other conditions that can cause pain and swelling in a joint such as the ankle. If there has been trauma to the ankle, a sprain could give the same symptoms.
Both. Break or sprain can both be very painful, swollen and bruised. If it doesn't improve with ice in the first 24 hours, i would recommend an x ray, which is the only way to really be sure.