My 1 week old baby involuntary move her hands and legs often, is she sick?

Probably not: Babies move a lot, even in the womb. Now that she is out, she's going to be moving her arms and legs quite a bit. They startle easily to sounds and abrupt movement. Some babies like being swaddled up so they don't fling their arms about and wake themselves up.

Natural response: One of the natural results of inactivity is loss of muscle mass.To prevent this in a baby, the brain sends out random messages to the muscles that trigger random movements. These start in the womb ; persist until the nerves link up brain control and allow purposeful movement.Some random movements will persist during sleep even in adults.