I have never really used this, or been blocked by this myself, but I would think that any P2P-program will be blocked from usage as it is just one more way of retrieving porn or ***ually explicit imagery and stories.

Limewire doesn't have Parental Control, just filters which anyone can turn on and off as they prefer. If you are a Mature Teen, as you say you have rights for, ask your parents (or admin) to allow you to use Limewire. If they are sceptic to what you may be searching for, you might allow for some rules, ie. saying when you are using the program, and allowing them access to where the computer is so they are able to check what you are downloading. Or other rules, like only using it when they unlock it, etc etc. The spesifics you really have to get straight on your own.

To me it doesn't sound like it's a problem with either firewall or connection when you mention this, but a program controlling the connection in much the same way as a fire-wall (denying access).

If this doesn't work, post back.