Dry skin can promote acne contrary to popular belief. Picking at skin can cause ulcers and sores which will blemish your skin. Applying a moisturizer and using only soaps that are gentle on the skin is helpful in this case. Drink plenty of fluids and water. Keep a trough of water or use a humidifier at home in your rooms. You can apply petroleum jelly and glycerine on your face at bed time. When choosing a moisturizer, look for oil-based creams and ointments. Fresh juice of tomato, cucumber and orange can be applied. Fresh cream too can be applied on face.
If these tips do not help, chances are that the dryness is due to underlying skin conditions like dermatitis, psoriasis etc. Vitamin A deficiency, hypothyroidism, Sjogren's syndrome, and diabetes too can cause dry skin.
Since I cannot examine you and know other related conditions you may be having, nor is a detailed history possible on net, I have listed the various possibilities that should be looked into. Please consult your PCP for primary examination followed by proper referral. Take care!