I am so sorry to hear of the loss of your pet. Usually, when you see a pet that has bleeding from the nose and the mouth, this is a signal that there was a blood clot or possibly an aneurysm in the lungs or chest. These are almost 100% of the time caused by a heart condition. Most of the time, these are not even known to exist and cats live with them for years and have no problems. We often see instances in addition to problems like you have - we see rear end paralysis also in cases of heart problems.
You do need to know that there is absolutely nothing you could have done that would have changed the outcome of your kitty's death as these things happen very suddenly and without warning.
Please let me know if I can assist further.