When it asks if you're sure you want to delete a database, and warns that all data will be irretrievably lost... you can always say no.
I think on the free hosting we're allowed 2 databases, and I know it's not enough for users with multiple applications who need one for each, but yeah. It might be a good idea to try and download a backup if you can, in the future. You can at least save the important stuff that way.
Sorry, but as @bdistler said, we do not offer backups to our Free Hosting customers. We do actually keep backups of our free hosting servers, but for disaster recovery purposes only -- we cannot restore a single account's files/databases from them (it's either the entire server or nothing)