I think she is coughing, not throwing up.
It's a good sign that the blood is not dried up, maybe she has been coughing so hard she broke some blood vessels.
Even if it starts as allergies it can turn into pneumonia real quick, so it's a good thing you are taking her in tomm.
Just my opinion, from my experience.
Good luck, I hope she is ok!
Bulldogs are angels in fur coats