It's "max_user_connections", and changing it won't help -- it will just change the kind of error you get from "too many things are trying to use the database server all at once" to "sorry, but your script has taken too long waiting for a database request, and we're shutting it down". You're sharing a server with thousands of other accounts, and an awful lot of them use MySQL (forums, WordPress and other CMS-based sites, as well as a lot of custom development). If your site needs more resources than a Free Hosting account has available to it, you're going to have to move to a less-crowded and better-provisioned server environment (Illuminated, Premium or VPS).