Since this has been going on for a few weeks now, and since you haven't gotten any relieve from standard home treatments, I think the next step is probably to have a doctor
look at this for you. You could go to see either your primary care doctor
or your dermatologist
, if you have one.
There are a few different possibilities here. The first is that these dry patches represent eczema, which is a condition in which the skin becomes dried out and inflamed, often also red and itchy. If you are vigorously washing your face, this might be contributing to the problem. The treatment of eczema generally involves a good moisturizer (you may need to use an ointment rather than a lotion) as well as a steroid cream to reduce the inflammation.
Another possibility is that this represents an allergic or sensitivity reaction of your skin, potentially to some personal care product that you are using. If so, thinking hard to identify which might be the offending product is important, so that you can stop using it. Otherwise, moisturizers and steroid creams, as determined by your doctor, are also important in the treatment of these conditions.
Set up a doctor appointment today!