Is it okay to start including non-lower back exercises?

[cuzimjj]

I've been out of the gym for a week because of a small pull in my lower back. This nuisance ended up hurting more to the point where I took a break. Now it hurts a LOT less and I only feel it sometimes or whenever I'm driving for 30+ minutes (but then again, anyone who isn't used to driving more than 30~40 minutes is probably gonna feel something in their lower back and need to stretch when they get out of the car).

So, what I'm asking is, is it okay to do NON lower back exercises. Hence, pull-ups, chin-ups, curls, dips. No squats, no deadlift, no overhead press, no cleans, and what about bench press?

[KobiDC]

If you don't feel any sharp pain, I wouldn't worry too much about it. Train using the exercises you prescribed for a week or so, or attempt your regular routine with decreased weight if your lower back still hurts.