I get tingle/numbness sensation in my left hand and pain/possible swelling in the right when i lay on my right side but not on left side or on back.

Neurologist: The problem which is positional, could be due to pinched nerves at the wrist(carpal tunnel syndrome) or impingement of a nerve or nerve root at the neck by a bulging disc or spur on a neck vertebra, but the latter conditions wouldn't affect both upper extremities. A neurologist is best qualified to evaluate you and order the appropriate tests.