Do you have muscle fatigue or weakness when performing your normal activities, or is it just when working out? If it is just with working out, as you suggest at the end of your question, then it is very unlikely to be anything serious.
Sometimes it can be common for people to have one side of their body be slightly weaker than the other. This is usually the nondominant side (left side in a right handed person, for example), and it simply reflects the fact that the dominant side gets more training and exercise during normal daily life. Usually the difference in strength is not enough to be noticed during normal activities, but working out may draw it out.
What this may also mean is that you are over training this part of your body, resulting in the fatigue, and you may wish to talk to your personal training about a more customized approach to fix this problem.
If you have more focal weakness, such as weakness in only the legs, or numbness
, tingling, or similar symptoms this may be a sign of a neuromuscular problem. However, it would be very unlikely for a neuromuscular problem to present with weakness of an entire side of the body (arm and leg) without other symptoms.