Do you squat, deadlift and row? Just curious. I find that many people with bad arms dont do the power building movements. The thing is as your whole body grows the arms just seem to follow. Make sure you are making gains in these areas first, then lets discuss direct arm work.
Im your height and have a 17" arm (flexed, dont know unflexed) at about 165lbs. Most of my friends just say they are sick. And Im not fat, probably about 10.5% right now. I think I had decent genes for arms, but nothing special. Heres the routine where I saw an inch growth over a 2 mos period. Is that incredible, not really, probably average, but this is what I did.
First, I hit triceps first as they make up a really big arm. You can have great peaking biceps and if your tris suck your arm will not look big in any shirt. Remember this. Okay, begin with a power movement for tris. So flat close grip bench presses. These should be done heavy in a range of about 6-8, you can use a smith if you like. Just make sure the stress is on the tricep. Next I would use some sort of french press. Most of the time this was seated dumbell french press. (both hands on one dubbell and elbows straigh up at the ceiling and at your ears, and lower the db to your neck, get a good stretch). On these work in the 10-12 range. Finally finish off with some sort of pulley work or dips for high reps in the 20 range.
As for biceps I always began with a power movement as much as possible. So for me this was straight barbell curls in a rack. Here Id go for 6-8 and do a bit of cheating, not much, but just little beneficial cheating. In between each set stretch. Grab something with thumb down, arm straight, and try to turn the inside of the elbow up to the sky. This should really facially stretch the bicep. Next exercise are seated preacher curls for 21s. Make sure these are slow and deliberate. Finally finish off with 50 reps of narrow grip chinups with palms facing you. Make sure to stretch all the way down and deliberately pull yourself up slow. It doesnt matter how many sets it takes, just get 50.
Id use this program for a month and see where you are, take a measurement. Make sure cals are high and the protein ample. I would only do this once in the week, as its pretty intense, and other things will indirectly work the tricep and bicep. Good luck,