Nothing you apply topically is really going to make the hoof grow faster, just like hair..good nutrition and exercise can improve circulation and that's pretty much it.
If she's not limping, don't worry about it. The part that was too long broke off, unfortunately higher than you would of liked. Wouldn't want to see it on a regular basis, but it's not the end of the world.No limping, no blood? No big deal this time. Horses that have nasty abscesses will break off huge chunks of wall sometimes and actually feel better once it's off.
Venice Turpentine is okay for painting the hard parts of the sole (never the frog!) as it's like a thin layer of varnish that will protect it temporarily until it's worn off, which is rather quick. Pine Tar will soften hoof, which could actually make it eaiser to break off, so personally, I'd just leave it alone.
Pretty much, if you are going to ride her in rough ground-large rocks, logs to step over, etc. a boot would offer some protection, but really for every day riding she's most likely fine.
If you are still worried, call your farrier or trimmer out to take a look and touch up the trim.