I'm sorry to hear about your unfortunate situation. Depending on the amount of damages you have incurred, I would consider hiring an attorney. The limited facts you have presented make it difficult to understand what, if any duty the City has in preventing your home from flooding. You state that the City owns the house, but I am unclear on this relationship. Do you have homeowner's insurance that covers flooding? If so, contact your insurance company.
As stated, depending on the amount of damage incurred, you may consider hiring an attorney to assist in your recovery.
Please be advised that the above answer is not legal advice. Legal information is not the same as legal advice -- the application of law to an individual's specific circumstances. My "answer" to your "question" is for general reference purposes and I recommend you consider consulting a lawyer if you want professional assurance that this information, and your interpretation of it, is appropriate to your particular situation.
More information is needed. Did the city give you a reason they would not cover all of our damage? Were you seeking damages beyond repair? I do not understand how a broken water main damaged your walls. Is you home at the bottom of a slope and the water main at the top of the slope? You should seek a attorney's assistance to determine if they are liable and, if so, for how much of the damage.
[Disclaimer- This information is provided as general information only and should not be construed as specific legal advice as this website is not intended to provide anyone with specific legal advice. No attorney-client relationship is created with the furnishing of this information. This answer should not be used as a substitute for fully discussing the factual nuances of your case with a licensed professional attorney in the state where you are located.]