This is a frequently occuring problem. When you remove the patch, immediately apply a moisurizing skin cream. If this does not give you sufficient relief, talk to your doctor.
The most common cause of unusual irritation under the patch is if you allow water to get in. If the manufacturer of the patch has not stated that it is waterproof, then avoid getting it wet at all costs. Even if it is waterproof, be sure that all the edges are sealed. Water leakage is a bigger problem for once a week patches than for twice a week patches.