Well, recently, I made a new friend, a language exchange partner (this is an online exchange, nothing odd, I think.), who lives in San Fransisco (I live in NYC.) For the first week or two, she didn't log on Skype a lot to talk to, but after the first day, she started logging on every day to talk to me. She doesn't like typing, so I always have to use the talk feature, which I don't like doing too much (because I need to worry about grammar). But I still used to it help her with her English.
We spoke to each other until Saturday and Sunday, when she is busy because she has kids to take care of. When she logged on Saturday night, she told me that she was crying because she thought about not being able to talk to me again (I felt really bad here, even though I didn't do anything wrong.)
Today, when she logged onto Skype, I said to her, "I don't like talking about those kind of things (feelings and stuff), especially when a woman is crying because I can't deal with it." Of course, she wanted to talk using the call feature. When we did talk, she was crying for an hour or two during the conversation, and started talking about her problems (mainly husband problems, like him cheating on her and how much she misses her country because of all the friends she has there.)
You normally wouldn't find anything wrong with this, right?
But lately, she's been really... clingy, I guess. The other day, she begged me to call her, even when I was mad at my mother, so I didn't want to talk. I was in a really bad mood that day, but she continued asking to call (saying things like, "just two minutes" or "just one minute"). I finally got annoyed, and asked her ot leave me alone for a little awhile. (this is the day before Saturday, when she logged on and said she was crying.)

I don't know what I should do. I'm no expert in love, but it feels like she sees more than a friend (asking for pictures, telling me to call her name, suggesting that she come from San Fransisco to New York for a play date, in which she'd go home by plane on the same day.)
I've thought about blocking her, and letting us go along our ways (she'll be sad at first, but I hope she gets over it), making a lie in an e-mail saying that I'll be unavailable for awhile due to loss of internet or something (she'd probably be able to see through it), or go through telling her how I feel about this.
She's a very good language partner (because she speaks Japanese to me like I'd like), but her clingyness and feelings weigh too heavily on me for me to want to continue.

What do you think I should do?
I'm terribly sorry for such a long post.