How can I gain back my mom's trust?

I apologize if this is lengthy, but I am sincere with this. Anyway, a few years ago when this began, I bought an iPod Touch with saved money. I was 13. I will admit, & I regret this deeply, I very much abused my right to the Internet, especially at my age at the time. I talked to strangers and sexted with them, among other inappropriate activites that would be a parent's nightmare to see their child engaging in. If I could go back in time to undo my actions, I would in a heartbeat. My mom found out after she took my iPod and inspected it. Of course, I felt my privacy was invaded and I was very, very nervous to await her reaction. I got my iPod taken away for a couple months before I could use it again. About a year after that, my iPod has started to malfunction and my dad bought me a phone (which I'm typing on right now, fun fact!) and I was so glad. Ever since my mom has taken away my iPod, I have been very clean with my actions and have truly changed, as talking to perverts is disgusting. I haven't done anything I'd feel nervous for my parents to see. Despite how I initially felt, I'm eternally grateful now that she did what she did otherwise I probably would be in a bad situation now. A week ago, she asked for my email and Facebook passwords and I gave them. I don't have anything to hide anymore, however I feel uncomfortable when people look through my accounts if you know what I mean. So, how can I regain trust and prove to her I have changed my online behavior? Thanks!:)