If a particular side of your arm feels weaker than the other, this could be a result of a traumatic injury, or a sign of nerve damage, or a repetitive strain injury, or even a blockage in the bloodstream. However, if you feel your sudden overly pain-sensitive feeling of the left arm is associated with chest pain, you may need immediate medical assistance. Otherwise, if it is just a general sense of weaker feeling that you have compared with your right arm, you could try unilateral training exercises at your gym. This would include single-arm shoulder presses, single-arm rows, and single-arm chest presses, which will help your left/right arm improve its muscle strength.