This is hard to answer without knowing how sensitive your files are. Think about it like this: how much is this data worth to you? If your data is worth more than what it would cost to switch to a proper hosting service, then you should just do that. Given what you are saying, it probably is, and you probably should.
I don't know what kind of data this is, so it's difficult to speculate on ways to protect it. If it's a sensitive customer list, maybe it should live on a well protected database. If it's sensitive personal information, maybe it should be encrypted. I just don't know without knowing more.
There are various ways of keeping people out of designated spots in any place on the server. My first instinct is to write rules for your server to follow. I imagine what you are trying to do is protect the files via .htpasswd on Apache. If that's the case, just make sure to have proper lock out rules, so that folks can't dictionary attack the site in a reasonable amount of time. There are other methods as well, but I'd still need to know what you were trying to protect first.
Of course, if you are on hosting where you don't have root access to the server, then you most likely can't edit the server configuration files. Again, the answer tends toward: buy more professional hosting.
forbidden public access? That Directory browsing is disabled or that they can't access the file even if they know the URL (e.g. guessed at
www.example.com/file.zip) due to
401 UnauthorizedHTTP response?