José M spanish solicitor.
In order to be sure where the damp comes you will need to contract a specilst inform.
With the inform you could sue the neighbour at court
Once we know that we have to spent dome money, we should study how we could save some
In order to save it, I recomend you to see your home insurance, here in Spain most insurances has legal coberture
If you have legal coberture, legal claains included, contact your insurance and tell them the problem
They will send you the specilist and you will save money, and if the damp comes from the other side, they will start the claim against them, and you will got your problem solved.
If you do not have the insurance coberture now, contract it and ster the procedure some months later.
I will be here if needed, thank you