Someone on omegle has hacked my facebook?

[Chelsea]

So I was on omegle just really bored and I was talking to this guy(video chat) im 14 and he was 17 and basically we just talked about school and stuff. the conversation turned a bit sexual and he asked if I did stuff and I said no, I said I didn't want to talk about that. He then said he's hacked my facebook and he will send dirty pictured and pretend its me if I didn't send him a dirty photo. I didn't believe him because how could he know my facebook?
Anyway I went onto facebook freaking out, changed my password and closed all the apps and stuff but then what freaked me out even more was when I went on my current session It was in Harwich, Essex. i dont live there so how could i have connected there? but then i put 2 and 2 together and figured out it must have been him on my facebook because he had told me he lived there. So somehow he managed to hack my facebook.
How did he do this? I didn't tell him my facebook or my second name
How can I make sure he doesn't have any access? should I deactivate my facebook before I risk being embarrassed by all my friends?
I'm done talking to people on omegle before you tell me not to. it was a stupid thing for me to do, I just needed someone to talk to.