You're limiting yourself to the number of exercises by only using dumbbells. But if that's all you have then these are my dumbbell suggestions for the upper arm:
Do hammer curls for the brachialis. It also works forearms at the same time.
Do normal dumbbell curls for the bicep. Use a narrow grip (dumbbells closer together) to put more emphasis on the outer bicep. A wide grip (dumbbells flown away from the body) puts more emphasis on the inner bicep. Use a neutral grip if you want to target the whole bicep.
Do preacher dumbbell curls to target the lower biceps. The preacher bench helps you stretch all the way to target that lower bicep.
I've found that incline dumbbell curls help target the upper bicep. You can feel that upper bicep stretch when the weights are at their lowest point.
One arm tricep extensions helps to train your stabilizer muscles because it's hard to keep balance while doing this exercise.
A two-arm overhead extension allows you to do more total weight than the above exercise because it's much easier to stabilize.
Tricep kickbacks help target the upper tricep. Hold the fully extended position for a second or two to target the upper tricep.