We had driving rain the past couple of days and water was coming in between the sweep and sill. Any suggestions?

Is the outermost door (I assume you have a storm door) flush with the sill on the outside... or in it set back into the frame?

If you do have one and its flush.. there are solid rubber sweeps that hang below the edge of the door that would seal out most of the driving rain... but if its set back... thats not going to work.

A lot of what is possible or not depends on exactly how your door is mounted and framed.

Outside mounted sweep, it the door is an outswing, or add an overhang or storm door. Hard to put a deep sweep on an inswing door.