It does sound like one of your plug wires is shorting, but since you just replaced them that shouldn't be a problem. I'd start by checking the distributor cap for any sign of damage, and look at it running in the dark with the hood open to see if its losing spark somewhere. If that doesn't seem...
If your new headlights are meant to work with the stock wiring on the car they should work fine, they will just be on whenever the car is running and the emergency brake isn't on. If you don't want them on all the time(which does greatly increase the life of the bulbs), check a wiring diagram...