Is it really uncommon to have a pulmonary embolism when you are young?

Usually yes: In general pulmonary embolisms (like most illnesses) are less common in younger people. Having said that some underlying illnesses (including having autoimmune disease, clotting factor mutations, sickle cell disease etc.) increase risk - so do smoking, hormones, infections and cancer.

Depends: Depends on what you define as young. There are well-known risk factors for pulmonary embolism which include immobilization that can occur at any age; smoking, birth-control pills, genetic predisposition, autoimmune diseases such as lupus, and cancer, to name a few.