Changed EGR valve and now giving Mass Airflow error

We just changed the EGR valve and the error code went away. But the car started running rough immediately and cutting off. We then got a new error code (P0110). We disconnected the mass air flow sensor and it ran perfectly. As we were working on the car, we noticed that one of the back-lights went out and the one of the front lights as well. So we began to think it may be a short. To get the car home, we kept the mass air flow sensor disconnected.

Question: Should we replace the mass air flow sensor or work on the short first?