E46 330 running rough

Any other warning lights appearing?

It sounds like the car has gone in to limp home mode.  If your garage isn't too far away then you should be OK to drive.  The chances are that turning the ignition off and back on should clear the warning lights and limp home.

I had a similar sounding problem with my old 330 a couple of years ago.  It turned out to be a combination of duff coil packs and throttle body.  I'd say the TB was probably a pre-existing condition as there were a couple of slight running issues in the lead up to the problem but the coil packs tipped it over the edge.

Diag read should point the way.  You may find that there are still errors after changing the apparently faulty pack as you may have more that one at fault.  If so, then you might be as well to change all six.  A little costly but they can often fail one after another when they start to go.

When the problem arose with mine, it started out that it would occur every couple of days and then the frequency gradually increased over a week or two.

Its always a slight relief when a problem turns out to be "just" a sensor, but sensor issues are becoming a bit of a PITA at this stage.  So many sensors on the more recent cars that can have such a dramatic impact on the way the car runs.