The first thing I would suggest is just gaining weight in general. I'm the same height as you and I would never have particularly impressive arms at just over 200 lbs simply due to my height and limb lengths.
My second question is how strong are you at compound movments for the triceps (like close grip BP)? If you are pushing 300+ for reps, then you might need some isolation work to get your triceps growing. If you are below this level, then you should probably try to get stronger at these movements and your triceps will likely grow.
Finally, what is your technique like on movements like close grip BP? Just because you move your grip in doesn't automatically mean you will use more triceps. You have to keep your elbows tucked into your sides as flaring your elbows out will bring more pec involvement into the movement.
As for your biceps, how strong are you at pull-ups, chins, and rowing movements? If you get really strong as these movements and throw a couple of sets of curls in at the end, your biceps will likely get bigger. Again, if you are weak at the compound movements, focus primarily on those and use the isolation work as a "finisher". If you are already very strong at the compound movements, then you need to focus more on the isolation stuff.