However it is possible that you had a transient rise in blood
pressure, resulting in
both headache and a broken blood
vessel somewhere in your respiratory tract. Put the headache aside for a moment, especially if it has not returned. The most likely problem, with
the combination of blood in your sputum and air travel, would be a pulmonary embolus. This is a blood clot in an artery of the lungs. Talk about this with
your doctor to see if there are any other reasons to suspect this problem.