If you turn on the points for the inner profile and look at the second set over here:



You'll see your profile kindof go back and forth ontop of itself, with a bunch of stacked points.

You can delete all but one of those points and it will extrude solid.

The other side has that too, but the profile is not buggard there. There are some other areas that I would clean up, but it's not really nessasary to the model.