Phone the uni on a number you know is them and ask whether it was them, first thing tomorrow. If it wasn't contact your bank immediately! Also keep an eye on your statements. If you want to be extra sure you could transfer all money out of the account you gave her tonight, if you have online banking.
In future, if you think someone may genuinely need details over the phone (always a good idea to avoid if you can) always ask if you can phone them back. Then you know it is who they claim to be. If it is really them they should have no problem at all with this.
Don't feel too silly though, it's easy to make mistakes like this!
xxx