What should I do if I get my adapter prong stuck in the outlet?
My recommendation is to talk to the apartment complex supervisor and get them to send out the complex maintenance person or applicable contractor to correct this problem.

It the broken off prong is sticking out of the outlet and it is on the mains hot wire side it can be a dangerous thing if someone were to touch it. Make sure to warn others about the potential danger until this is serviced / replaced. If there are small children in the unit make sure that they have no access to that area as well.

Outlets are a relatively low cost item and in all likelihood the service person will replace the outlet with a new one.