Girls, DO YOU THINK SHE IS AVOIDING ME or am I overhtinking?

I think she's just busy and stressed. I mean she could have just not turned up but she didn't, she let you know that she was unable to make it and why. I think your issue is that although it was just hanging out, you wish it was a date. Am I right? So ask her on a date. I bet she'll go with you. Text her and say that you hope her time with her mum went well and that her paper is going well and that when she's free you'd love to meet up. Good luck.