I got a bloody nose while throwing up as well. My doctor says its normal, and that stuffy and bloody noses are common while you're pregnant.
Here's some advice from the MedHelp website and our I'm Expecting app on morning sickness AND on nosebleeds. You can find this in the app by going to the Pregnancy Diary from the home screen and selecting Morning sickness or Nosebleeds from the Symptoms menu. Then click the menu bar in the upper left and select Symptoms Manual to see your symptoms.
Hope this helps you understand what you're going through!