Is severe itch a common side effect of discontinuing zyrtec (cetirizine)? If so, how long will it last and what can I do to cope?

It is not. Presuming that you were taking zyrtec (cetirizine) for the itching, the itching would return when you stop taking zyrtec (cetirizine) unless you can eliminate the cause for the itching.
Itch. Usually it is not a severe rebound effect but I am sure it can happen. Depends on how much you were taking and what for. Try to decrease by only 1/2 tablet every other day to see if you can titrate off. Or see the specialist who prescribed for direction.