It is possible that your headache after exertion is related to your asthma. Indeed, it happens that people develop a headache because they do not breathe adequately. This is what happens when people who are not used to it make a vigorous effort by cutting their breathing too abruptly or for too long. In your case, your asthma (and the scars of your embolisms, to a lesser extent) can make it difficult for you to oxygenate your body (and your head) properly. One way to test if this effect could be the cause of your situation is to take Ventolin about 30 minutes before the effect and try to breathe more deeply and regularly. I also recommend that you ask a doctor so that together you can get more information on this subject. Have a nice day,