What it means if my friend is "obsessed" by me?

Anonymous
I met a girl a few months ago in Internet, we started talking and we began joking like we are a couple and i played role of boy. And now we finished this game, but still talking and she sometimes says "with who are you chatting?", "stop chatting with someone else except me", "im jealous", "You're my property", "im sad because u are busy and dont write me, but i always think about you"
But she said she isn't a lesbian. And.. Um...
What it means if my friend is "obsessed" by me?
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