A new relationship- is it going OK with her?

I recently asked a young woman out, she said yes, we went out yesterday. I paid for her drink (she began protesting but then seemed to accept it with a smile), and we talked. She seemed to try to share my interest, despite me knowing she didn't have much interest in it. At the end, I asked her out again, she said yes, then said she would write me about it.
I met her today, we were talking, at one point she wanted to show me something I asked, grabbed my shoulder and tried to push me forwards to show something unnecessary, was very supportive and encouraging, etc.
Towards the end, we just talked, she showed me her horrific schedule for the week on her phone, then she began talking to someone else, and neither of us said goodbye to the other as a result. I then approached her friend (the girl I went out with was nearby) and discussed a few things with her. When I waved and left, I heard a faint 'bye'. Towards the end, when she and her friend were standing next to each other, she was barely talking to anyone.
Is this going OK? Do I have anything to worry about?