I live in anxiety and I've had this happen. Either laughing until tears or laughing that brings on a release of crying. I think it just opens you up and things sneak out as they need to? Laughing/crying actually don't sound all that different or look all that different. For me they are frequent partners. When I'm crying I will sometimes start laughing too. I burn off a lot of my anxiety/emotions with laughter. Hopefully your family won't think you're nuts. That kind of thing just happens sometimes I think.