Dizziness might be associated with a fever, but coughing up blood...call 911! You don't cough up blood from a cold or the flu!
And get some exercise when you're well again. The best way to get your immune system healthy is a good cardiovascular workout a few times a week. Without exercise and paced, moderate to heavy breathing, your lymph won't circulate as well as it should. A healthy lymphatic system means a more healthier you.
But seriously, don't mess around with the blood you're coughing up.