Neighbors leaking pipes have caused damage to my brownstone.

I have noticed a strange dank smell in our house for the last two months. On returning from a 2 week vacation I noticed major cracks and bubbling of the plaster in the party wall. I ran into one of the tenant who rents next door and he informed me the landlord had recently repaired major water damage to his two floors but had not fixed the plumbing. Within a week of the repair to the walls, the water damage is appearing again. I called the landlord to explain the damage to my walls and he denied any problems with his units and claimed he had not done any repairs recently. I haven’t called my insurance company yet, but I need to get my walls fixed before my wife gives birth in 7 weeks. If we meerely patch it and he does not fix his pipes we are back to square one. Any advice would be much appreciated from fellow unhappy homeowners or lawyers.