Finding Strength in Patience After False Accusations

Assalamu Alaikum everyone. I'm dealing with a really tough family situation right now. My household has a lot of tension, and today my parents were having a major argument, which led to my brother and me getting into it as well. He has a history of serious sins, and unfortunately, his behavior is often violent and aggressive. He starts fights and insults family members, including our mother and me. I always try to be patient and avoid engaging, but sometimes it's so hard not to respond. During today's argument, he made a terrible false accusation against me in front of both my parents and another sibling. He claimed I had been sneaking out to meet someone, which is completely untrue. I defended myself as best I could, demanded proof he didn't have, and even swore by Allah and offered to place my hand on the Quran. Alhamdulillah, my family didn't believe him, but I can feel my mother's doubt, and it changes how she looks at me. That hurts so much. I have never done what he accused me of. I don't have any non-mahram male friends or involve myself in such activities. I've worked hard to earn my family's trust. I just needed to share this and ask for your duas and advice. How do I keep holding onto my faith in Allah and practicing sabr when this feels so overwhelming? Jazakum Allahu khayran for listening.