I quarreled with my boyfriend and sent an apology message. He never replied. Do I need to send anything else, or should I just wait?

I don't think we should send him again. Let's wait and give both sides some time to think calmly, because when he is angry, he doesn't want to answer anything you send him. After he calms down, he can fully consider the problem and have a satisfactory answer on how to solve it.