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 .
Al-An'am : Ayah 152
...We do not charge any soul except [with that within] its capacity....
Here's a hadith to suit your condition though not fully relevant
Sahih al-Bukhari, Sahih Muslim, Jami' Tirmidhi, etc.
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:
Unintentional swallowing of toothpaste during fasting.
One more fatwa which is most relevant:
A fasting person swallowing blood during sleep.
All these say just one thing : The fast is not invalidated when anything is swallowed unintentionally.
answered Aug 6 '13 at 21:29
