With no medical specialist, and particularly no diagnostic imaging available, the local doc will not be able to make an accurate diagnosis - the part of your back that you injured is laced with myriad muscles, connective tissue, intervertebral discs, etc., any number or injuries to any of which could produce the symptoms you described.
The first poster has it right - best case is a severe muscle strain. The fact you could barely stand up in the rack suggests its a relatively bad one. Worse is a disc rupture. Worse still is disc rupture and muscle or ligament damage.
The main thing is to rest it as much as possible, see what the body’s normal healing process does over 10 days. The dumbest body is smarter than the smartest internet therapist. But since you asked . . . Forget ice - that’s dumb. It reduces circulation and swelling - the very things your body is trying to do to immobilize and pump repairing fluids and cells to the injury site. If anything, heat it with hot water bottles etc. And forget the lacrosse balls, massage, stretching, etc. - for the same reason you’d be stupid to rub a raw blister - you don’t need any more mechanical force reefing on already torn tissue - that’s what got you into this mess. Don’t make it worse. If in doubt, assume that it will make it worse. If you are going to do that stuff, save it for when the tissue you are working on no longer has a nasty bleeding gash running through it and your entire CNS is all but screaming at you to leave it the hell alone.
If its much better in 10 days, great, it was a muscle strain. Wait until it is completely pain free - CNS no longer screaming at you – then and only then, return to training gently over a couple of weeks. If its not much better in 10 days, its more than a muscle strain - you’ve queered a ligament or disc or both. And if that’s the case, you have to get off that island, and back to a competent orthopedic spine specialist in Oz. Anybody who tells you they can tell what the injury is by looking or feeling it with their fingers or having you bend your legs etc. is blowing smoke up your ass - educated guesses at best. You’ll have to have appropriate diagnostic imaging (MRI, discography, etc.) for anyone to actually see what is injured, where, and how. You’ll be looking at months to a full year or so before you are back to your former self. Back injuries, when serious, are just awful things. But they do get well over time. Been there, done that, don’t want to do it again.
Just don’t stop lifting or let this make you afraid to do squats, deadlifts, etc. Your injury almost surely happened because of too much loading, too soon. You can fix that when you are back in action with better programming. The best thing in the world for your back is to get it strong as hell and keep it that way - especially so now that you have had an injury.
Hang in there, this too shall pass.