my first (water birth) the 'erge to push' was overwhelming, and my body just did it (no conciousness on my part), I concisously didn't add to my bodies natural push...i didn't want to rush and tear.
My second (on my knees on a bed), I wasn't conciously pushing...and it turned out I needed too. Two very different births. Both wonderful in their own way.

You may find hanging on and screaming works for you again, you may find you need (or just do) something else. You do as you need to do...

xo