Hey bro,
If i was u and u said u hurt your back i would stay light if u feel like u have to lift. I would let it rest if i was u but a dogs a dog and i would probably train on it to but nothing bent over i would stick with pulldowns wide and close grip if it hurts stop immediuately and go home and
ice it. Continuing a workout while your injured will only make it worse i promise.
Good luck with everything and if its hurts let it HEAL i dont wanna see u gettin hurt bro. Usually an injury isa sign that u need some rest anyway. i think thats why i got sick i was overdoing it and i didnt stop.
Peace n Godbless u bro