It sounds like you may be having an isolated muscle twitch, especially if the twitching does not make your whole arm move or tremor. Isolated muscle twitches are very common, and they are usually caused by fatigue or muscle exertion. Therefore, most people will notice them after vigorous exercise or when they have not slept for a long time. In these cases, they tend to go away after resting properly or giving yourself a few days off from exercising.
It would be unusual for an isolated muscle twitch like this to be a sign of a serious medical problem. However, if you are having twitching in multiple different muscles of the body, or if you have a more generalized tremor or any evidence of trouble with muscle strength or with coordination, these might be symptoms of a more serious muscle or nerve problem that would require medical evaluation.
Regardless, having this issue checked out by your primary care doctor
would be a good idea. They can take a look at the affected area and make sure that there is nothing that you need to be worried about going on!