I have hooked up my lines for my ice maker but now that I have it hooked up there is water coming out from the filter. Could needing a new filter cause it to do that?

You may need a new filter, but I doubt that is causing the problem. Look closer at the connections.

Is this an internal filter or a filter on the outside supply tube?

Trace your supply line coming from wall. I do not know the situation with the filter. Just follow the line until you come to the leak. It's very simple most of the time.