Girlfriend never offers to pay? Is she using me?

We've been dating for about 3 months. She is really great and I like spending time with her, but I sort of get the sense that she's using me. She hasn't offered to pay for anything at all. I have no problem paying, but I don't like that she just expects me to. She is the first girl I have dated so I'm not sure if the things she's doing are normal. Here are a few:

- The not offering to pay thing
- She has canceled 4 or 5 times last minute, but then calls back really enthusiastically to reschedule
- Seems disinterested in what I have to say half of the time
- She's very distant for a few days and then all of a sudden she won't leave me alone
- I bought her a really nice dress ($400) for an engagement party that she didn't even invite me to

The last one ticked me off a little. All in all I love spending time with her, but I don't want to invest so much time and money into this relationship if she's just going to walk out on me. She is very attractive which makes it very hard to be objective when I'm around her.
Girlfriend never offers to pay? Is she using me?
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