When it came to building arms, I followed some pro workout routines and took advice from some BBs at the gym
Basically you need to hit the bicep long and short head with a barbell and dumbbell movement. The basics will be barbell curls (arms at shoulder width), dumbbell curls on the preacher, but with maximum contraction at the top of the movement for your short head. my wrists used to hurt and forearms hurt too, but that's because thr were weak. Keep doing them and get them stronger
Then for more long head interaction, use an incline bench at 40 degrees or so and let your arms dangle as much as possible to gett the long head stretched, a light weight is all that's necessary. If you have a bicep Machine with incline pads, even better.
There's not much more than that unless you want to get into the peak, but then you need to use one side Of the cable machine, hold onto the other, make sure the elbow of the arm you are working stays parallel to the ground, and pull until you bicep is fully contracted then release until your arm is fully stretched
That's the basics, there's a lot more you can do, but unless your in competition, there's no point and it's a waste of time to do. Don't worry about pullups for your bicep. Do them in your back day
I'm currently sitting on 22" arms,not that much body fat of my bicep either, 12 weeks and see the progress. Guess it worked for me