Is this her way of saying "no" to me?

Don't freak over one incident. If the next couple of weeks she keeps coming up with excuses then you can conclude that she doesn't like you.

Sometimes people make EXCUSES to get out of situations and it make it hard for you to trust them, other times they tell the truth. She may really be having health problems. A way you can tell she don't want to hang out is if she keep making excuses and scenarios to why she is busy, she don't call back in 1 week or so update you on how things are going, yet it all take time and being patient. So in my opinion it may not be a way of saying no

Dig for evidence before you make your next move. Medical emergencies are the best excuses to give because of the exact reason you gave. You don't want to call someone out on something that could be really serious and you are wrong. I always smell bullsh*t when someone gives that answer but that's because I don't trust anyone with a heartbeat.

I say give her the benefit of the doubt. I had to turn down a guy that I was literally crazy about on and off for 2 years and he finally asked me out, but my grandpa was in the hospital and given about 2 days to live. So I gave the excuse that I can't go out because of a medical emergency in my family. Wait till everything passes and see what she has to say, sometimes you just have to be understanding and go into things with an open mind. Good luck

Ask her to meet up another time and if she rejects your offer for the 3rd time then forget about her and move on

If there is genuine love, anything can be fixed.