Is it bad to spit up blood after a nosebleed? The weather is what caused my nosebleed.

Proabbly not. it's very common for blood to go down the throat. One small bleed that stopped promptly is not a big deal and not a reason for medical attention. If it keeps repeating or is a cup or greater, that would be a reason to see what is happening. Blood leaks, comes up. temporary then not a problem.