Well it depends on how much time has gone by, and whether she has another boyfriend. If you still want to get her back, you might want to just talk to her about it. First you might want to say something like "I can understand if you dont want to get back with me, but I still like you a lot, and I want you to hear me out". Tell her you lied about the flirting thing and apologise. Then tell her about the problems you had with your family, and how you were really stressed out and not thinking straight. Reinforce the fact that you would really like to be with her again, but give her some time to think about it.