CT - when you work your chest, your triceps get a workout, too. When you work your back, the biceps get hit some.
There's no one answer to your question. It has to do with your overall program design.
For example, if you are doing a 2-way split, you might do chest/triceps/shoulders one day and back/biceps/legs the other, then rest a day, then repeat.
But if you were doing a more complex split, you might do chest/biceps on day 1, rest day 2, back/biceps on day 3, shoulders/legs on day 4, rest on day 5 and repeat.
The important thing is that you not work the same body part, directly or indirectly, on consecutive days. Give it a chance to recover.
In some cases it's not essential to work your arms directly at all - focus instead on the larger muscle groups - legs, back, chest - and let the secondary effects take care of your arms. This is particularly true if you only have time for a full-body workout 3 times per week.
You're slender by most standards. If your goal is to increase your overall mass, I'd focus on nutrition and do a stripped down full body workout three times a week, concentrating on the large muscle groups. Working hard to stimulate growth in the legs, back and chest will have benefits to your arms as well.