Why do I get swollen red, dry patches on my face regularly?

There are several possibilities here, and since this is a problem that you have been having for a long time I suggest talking to your primary care doctor to see if you can arrive at a diagnosis. The most likely possibility is that you have eczema. Eczema is an inflammatory condition of the skin characterized by dryness, redness, itching, and scaling. Sometimes eczema flares up in response to things in the environment (dry weather, chemicals and other things you may come into contact with at work, etc). The mainstay of treating eczema is moisturizing. It is always best to use a thick "greasy" kind of moisturizer as these are better at trapping in the skin's natural oils and moisture than typical lotions. Stubborn areas of persistent redness or itching can be treated with a small amount of an over the counter topical steroid cream. Another possibility would be rosacea, which is a redness of the skin of the cheeks and other areas associated with dilation of small blood vessels under the skin. It is often treated with topical or oral antibiotics. I suggest talking to your primary care doctor to have a firm diagnosis and decide which treatment option is best for you.