Is it pretty common for raynaud's phenomenon to occur on only one side of the body?

Usually symmetric. Raynaud's disease is due to spasm of blood vessels supplying the fingers and toes, and sometimes other parts of the body. Symptoms are usually symmetrical. People vary in the symptoms they get with any disorder, so it is possible that a person could have symptoms on only one side. There may be a difference in circulation to one side of the body. A primary care or rheumatology doctor can evaluate.
No. Usually bilateral more commonly upper extremities some secondary concerns: unilateral thoracic outlet syndrome prior trauma some other local vascular issue consider vascular surgeon consultation.