What causes the labia to swell?

Anything... ...From an allergy to a lubricant or condom component to simple friction. If this is a significant and/or persistent problem, you'll need to see your gynecologist.
Couple of things. Infections, allergic reactions are probably on top of the list of causes. If just swelling without pain, more likely allergic. If painful, with blisters, ulcers etc...Infection such as herpes could be the cause. Check with your doc.. Good luck.