Can you take a picture of the shared area? Again, around here, on houses I inspect int he typical neighborhood, two houses share the same side swale that is supposed to run the water off the property (usually to the street in front, but sometimes to an alley in the back.) With a couple exceptions (McKinney lets water drain across back yards down a whole street,) they are not ever supposed to run it across yards or back to a neighbor.
This is one of the most common problems I find because builders to do not get enough grade to the street in the swale or they grade it poorly and create high and low spots.
If it is a shared side yard situation, I would say your builder has as much responsibility as the neighbor. It is common for the drainage characteristics to change when the house is built next door. When it is two different builders it can be a mess.
Not sure you can win in court. In my neighborhood, the city had to spend millions to improve the drainage on the city golf course (that is in our neighborhood) because the builders/developers/someone graded most of the golf course lots to drain to the course instead of the street as called for in the city rain water management plans. So the golf course flooded all the time. I am thinking that if the case could have been won, the city would have sued the builders/developers/someone.