Do I need a new trailer hitch?

If it's the original (factory) hitch on your 04 GM, I'd replace it.
That era GM hitches were problematic from the get-go....rust or not.

Is the receiver itself rusty or just the draw bar, ball, distribution bars, chains etc? Rusty welds and bolts on the receiver could certainly be a serious problem if severe. Surface rust on the other components is less of an issue. If welds are and surface are not compromised by the rust then lightly sand them and put a coat of paint on. A light rust inhibitor coating wouldn't hurt.

Carefully inspect the welds and bolts. (Which should be done before towing anytime.) They will all get rusty over time.

Based on past failure records of that stock GM hitch I would replace it no matter if it showed rust or not.
Note especially this post, and this one.
Barney