Have you tried working your arms (both biceps and triceps) alone? Could you be wearing them out on the lifts that you are doing prior to arms?
Give super sets of a bicep movement followed by a tricep movement a try. Go back and forth for a few sets, then switch movements.
Try this: Superset your standing barbell curls (keep a narrow grip, with your arms pinned to your sides) with close grip bench. Then switch to French presses (a.k.a nose-breakers, again keeping elbows in tight and pointed toward the ceiling) with seated alternating DB curls on an incline bench (keeping elbows close to your torso and slightly behind you). Then finish up with wide grip preacher curls and DB kickbacks.
This routine gives you the chance to work your biceps varying angles.
Focus on form before piling on the weight. Do this twice a week for a few weeks, then change up the moves.
Also, eat a big bowl oatmeal about a 1/2 hour before going to the gym to fuel your workout.
Also, if you want to get good at pull ups and chin ups, you have to do them. Start with neutral grip, they are easier when you are starting out.