What is the cause of major labia majora and minor severe swelling?

Trauma,infection mor. Commonest causes are infections, blunt trauma, insect bite, and allergic reaction.I will suggest you have it checked by your doctor or gynecologist.
I would worry.. About infection. But you did not mention pain/ if the swelling is acute (over a few days) i would see your pcp or gynecologist quickly!
Trauma, infection? Many possible causes, they are infection, trauma, etc., ...