The majority of homeowners insurance policies do not provide coverage for flood damage. Unless your insurance policy provides coverage specifically against floods, you would have to have flood insurance through FEMA or the NFIP.
Coverage & Claims
For the purpose of getting your belongings replaced as quickly as possible, I would definitely recommend contacting your renters insurance provider immediately. While your neighbor will likely be considered liable for the water leak, your insurance company should be able to act quickly to replace your items and even provide a temporary place to stay while your apartment is being repaired. Your insurance company will likely subrogate with your neighbor's company for your personal items, but that should have no affect on your ability to receive compensation for your loss.