If you have dry patches on your face that become red and irritated when you apply moisturizer, it could be due to dehydration or a flare-up of eczema. To help improve your skin, make sure to stay hydrated, increase your water intake, get plenty of rest, and continue moisturizing your face at least twice a day. Opt for mild, fragrance-free moisturizers such as those containing ceramides. If the eczema persists after a week of moisturizing, you may consider using over-the-counter hydrocortisone cream. Don't hesitate to seek further advice or assistance with your skincare concerns.