In that situation it seems like you're really pushing just to protect your hand on a board that probably missed the other player more than attempting a stop and go. Stop and go's involve you choosing to go all in on any flop BEFORE the flop.

Also, the stop and go's most valuable purpose is to push hands that are better than yours out on a flop that missed them, and in this situation it is almost certain that you will get called by any higher pair, which are what beat you, and maybe get a fold from the hands you are ahead of, which are overcards.