It sounds like it's your spinal erectors and it's a problem I have struggled with before. It is usually taller people who have this problem and it's aggravated by tight hips, glutes and hamstrings. If they are tight they pull down on the lower back and put a lot of force on two small muscles. I would look to Kelly Starrett (I HIGHLY recommend getting his book, it will save you lots of money and time finding cures to injuries), he also has some good videos on youtube.
A good way to strengthen these muscles is doing Romanian deadlifts. I would drop any exercise that is hurting your lower back (Squat and conventional deadlifts are usually the two most common).