A belt, when used properly, is not for your back. It's for your gut. Prior to your lift you should pull air into your gut and push out against the belt. This helps you to have a solid core.Think of a wine barrel with copper hoops. The hoops keep the barrel strong, its not there just to support one side.
Sounds like your SI joint went out.
Don't "forget deadlifts". The are the most important lift you can ever do. Yes, more so than squats and sure as hell more than bench. It's a full body exercise. Why do most powerlifters hate deads and/or suck at them? Cos they are the boss.
The heaviest weight ever squatted was done with shit loads of support gear. The world record deadlift (460kg) was done in shorts, slippers, T-shirt and belt cos support gear don't work much with the king of lifts. Deads will thicken you up, train your core like nothing else (try doing ab work after a proper deads workout), work your entire posterior chain from the soles of your feet to your neck, plus your quads, abs and grip. Do them and you will have girls throwing their panties at you. In a good way. Any dipshit bro can get big arms. But walk into a room with a set of Italian salami traps bunched up dere, a thick back, big hamstrings and forearms like a ships anchor rope and you gonna have guys giving you space and girls wanting you to father their children. Right now.