I've been sick for a few days with headache and sore throat with pain and cough. Today I was coughing blood. Should it worry me? Is it contagious?

See a doctor. Coughing up blood can be non-serious (blood from dried out nasal passages) or it can be serious (bacterial infection in the lungs, cancer). I would get seen by a doctor, possibly get a chest x-ray and treatment for whatever the underlying cause might be.
May be-need to check. Airway irritation/ inflammation is the most common cause of coughing blood. Unless it's large amount, this should be self limited. However, if persists, definitely needs to be investigated further, As for being contagious- really hard to say, as viral respiratory infections usually are, but limited.

Related Questions

Sore throat, stuffy/runny nose, headache, chapped/bloody lips, coughing up blood. What's wrong?

URI. This sounds like a common cold with broken blood vessels in your nose, throat or lungs: you must be seen immediately for examination and evaluation. Read more...
You need exam by Dr. Coughing up blood should never be ignored and should warrant an office visit or at least a phone call to your physician. A normal cold will not usually result in coughing up blood unless the coughing was very prolonged and severe. Even then it's best to speak with your physician as it is one of the warning signs of lung cancer. Chelilitis is the term for inflammation of the lips. See: http://bit.ly/1pgW3B4. Read more...
Get Evaluated. You could have a bacterial or viral infection.See your PCP or go to an urgent care center or ER immediately. for evaluation and treatment. Read more...