Pulmonary Embolism Support Group
By far the most common form of pulmonary embolism is a thromboembolism, which occurs when a blood clot, generally a venous thrombus, becomes dislodged from its site of formation and embolizes to the arterial blood supply of one of the lungs. Symptoms may include difficulty breathing, pain during breathing, and more rarely circulatory instability and death.

Even though I have two copies, I didn't have a clots till I was 61, and that was after a very long ( 13 hour) drive.
Hope all goes well with the doc visit.
FVL can be tested for while on anticoagulants. You're right though that other hypercoaguable conditions like protein S and protein C can't be tested while on anticoagulants. Here's a brief article abohttp://www.mayoclinic.org/diseases-conditions/factor-v-leiden/basics/tests-diagnosis/CON-20032637ut the subject.
I had a strong family history of clotting, so it was decided to test for the things that could indicate higher clotting risk. If those came back clear, then I would have the other tests that have to be done once after I came off anticoagulants. When I came back homozygous fvl, it was recommended that I stay on the anticoags "indefinitely".
Hope this helps clarify things.