Can I continue to work out with a back injury?

A few weeks ago I decided to up my weights from 25 to 30 lbs on the barbell. I take a few strength training classes where we do tons of reps. I guess my form wasn't very good with the increased weight because my back was reallly sore after a few classes with new weight. It must've been the deadlifts. So I skipped one weights class to give my back a rest. When I went back for another class, I tried to be very careful with my form and even dropped my weight down to 20 lbs because my back still hurt a bit. I realize that this weight is next to nothing, so I feel like a total dork for hurting my back like this. I have never had back issues before. After the last class, I could barely take a step without my back shooting into spasms. I skipped cardio the next day since I could hardly turn to look behind me and I've only taken a pilates class since then. Tonight, I'd normally take Zumba which incorporates a lot of core twisting moves. If I stay very low impact and don't do the twisting moves, I'm hoping I won't hurt myself again. My back is still a little sore, but I'm sick of not working out. Tomorrow is my normal strength training day and I'm thinking I'll have to skip again.:sad:

The question is: Is it better to not work out at all until my back is not sore anymore or is it better to continue working out and just take it easy? I really don't want to be in the pain I was in last Friday, but I also don't want to get fat and weak waiting around.