Can build up of cholesterol in the carotid artery be causing lack of blood flow in the brain and could that lack of blood flow to the brain cause symptoms in the arms and legs such as cramping, aching and heaviness?

No, those symptoms are not correlated with carotid artery stenosis. The ischemic stroke due to carotid artery stenosis causes unilaterally symptoms (loss of motor and/or sensory function) from the opposite side.

At age 35, unless you suffer a genetic disorder affecting lipid metabolism or vascular anatomy, would not expect carotid stenosis, or a stroke risk. Brain hemodynamics would not influence presence of cramping in the limbs, in absence of spasticity.