If you have your own insurance that is the way to go. You have been told the correct thing. You need to show the people in the other apartment were negligent or you can't make a case against them.
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Try your own insurance company. You can also sue the other tenant and the owner of the building. You have the burden of proving liability. You will need to prove what caused the accident by having an expert testify, the fire Marshall would be helpful.
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