Yes, you can take a shower. Be mindful of your contractions though. My water broke at home at 2am with my first and contractions didn't start for about an hour, and I ended up eventually needing pitocin to really get them going. I was in labor for 21 hours.
With my second, my water also broke at home at 2am, but contractions started immediately and were 5 minutes apart from the get-go. DD was born 3.5 hours after my water broke.