Did you get an ASA badge or just a pledge pin? I can't say 100% for sure, but I'd bet my bottom dollar if you were initiated, you'd know. I bet you went through some sort of a colony/pledging ceremony.
If you didn't get a pin that looks more or less like this, then you aren't an initiated member.
To make double sure for certain, you can always contact ASA headquarters and ask them. And if you were not initiated, then you are welcome to join another sorority.