It highly depends on exactly what the City did or did not do, whether it was done by the city itself or a contractor, what damages it may or may not have caused, and - frankly - the city's view of its responsibilities toward property owners.
If the City did the work itself, it is likely to be immune from suit under sovereign immunity theories, but there may be exceptions to that in Ohio.
There may also be a lot of room for dispute about exactly what was required and why.
I would suggest you start by raising this to the "right authorities" and then to you council member. If the City won't address it, you can consider hiring an attorney - but it may very well cost you more to sue the City than to simply fix it yourself, and you still may lose.