Do not beat yourself up!!! You don't have a crystal ball. What if she had driven and had an accident - then you would be saying, "why didn't we walk". And even if she'd driven, she might have slipped on the ice in the parking lot or walking up to the clinic. There are a million scenarios that you can create.
This was NOT your fault, it is just the unfortunate way things happened. Be there for your sister - she will need you now - I know you will be the best sister/support!!!
I hope all goes well for her!