My sister bled from her nose today, and due to excessive bleeding, she happened to accidentally swallow some, she later coughed it up, but there is no reassurance that she spit it all up or not, does swallowing this blood deem her fast invalid?
If your sister tried her best to cough out every bit of what she had swallowed, Allah is aware. If she wasn't successful, still Allah is aware. If she had tried her best, that is enough for Allah .
...We do not charge any soul except [with that within] its capacity....
Here's a hadith to suit your condition though not fully relevant
The Prophet said, "If somebody eats or drinks forgetfully then he should complete his fast, for what he has eaten or drunk, has been given to him by Allah."
And if you think your sister's situation is very similar to swallowing traces of toothpaste while brushing, here's a fatwa:
One more fatwa which is most relevant: