Call an ambulance. Or get a friend to take you. You need urgent medical evaluation.
Talk. Talk to your mom, talk to your pediatrician/family physician.
Clotting tendency. Elevated homocysteine levels are usually due to a lack of frolic acid and other B vitamins. Chronic elevation can increase the chances of hardening of the arteries as well as increase the likelihood of blood clots. Dietary modifications and exercise can help protect from some of these problems.
PE. A small pe might go unnoticed but any significant sized pe is going to cause symptoms which would either get your attention or worse. If you suspect pe you should get to the er.
? hospital. Pulmonary emboli are often small and unrecognized. Even with minor symptoms, they can often be treated as an outpatient. Only large and symptomatic pe "force" hospital treatment. Blood thinners are the most common form of therapy.
Yes. Patients with cancer are at a greater risk of developing blood clots. Ask your doctor about compression stockings that may reduce the risk clots in the legs. Also, I recommend to get up at least once an hour to walk around the plane.
Yes. Cancer is a well-known risk factor for blood clots. If the flight is short (which is relative these days with the long wait times, security etc), the risk is not so high but particularly with longer flights, ask your doctor for prophylaxis - she can get a blood-thinner shot beforehand. Oxygen requirement is another issue as there is less oxygen at altitudes. Consult your doctor!