How do I keep runoff rain from flooding my carport?
Assuming you can't get the political problem solved (letters to the editor time, perhaps), you need to address the part where "driveway sits low so all the rain comes in like a river" (though you might also take the practical citizen approach and see if there's anything blocking the ditches and drains that you can, as concerned citizen, remove on your own.)

You'd be looking to build a smooth, drive-over-able, dam across your driveway. You may need to extend it with smooth, mow-able wings onto your lawn/yard. Alternatively, you make a wide smooth ditch that you can drive through, again extending of into the yard so the water has somewhere to go. In either case the aim is not to "just stop" the water (that is a game you almost always will lose at eventually) but rather to divert the water around your house/carport to somewhere less problematic.