During the reversal, it is thought that Earth would have multiple magnetic poles (much like Sol). These would gradually move over the planet resulting in effects as benign as auroras over the equator, or as disastrous as telluric currents powerful enough to ruin electrical infrastructure.

> say I'm heading South

After the reversal is complete, yes. During the reversal your compass could well be rendered useless (pointing toward your closest pole); assuming we're right about how the reversal would happen.