If an argument between you and your brother progresses from mean looks to a fist fight, you could say that the tension between the two of you escalated. To escalate is intensify or increase quickly.
When you see this word, picture an escalator that takes you up to the next floor quickly. But remember, there's something you don't like on that higher level because it's usually bad if something escalates. Prices escalate when something becomes scarce, be it a popular toy, a concert ticket, or food during a crisis. And if a war or conflict escalates, it becomes more intense and violent.