Physiotherapists and chiropractors are basically the same. If you go to a physiotherapist, he will most like do some chiropractic adjustments on you.
I went to a physiotherapist after my back went out about a year ago. After weeks of visiting him, I only really started getting better after he did some adjustments on my back. I would definitely recommend doing the same though. Your back gave out because something moved out of place. It needs to be readjusted.