It sounds like your dermatologist
thought that this was some sort of allergic or contact reaction of the skin, which is why they prescribed a steroid cream. I do think that this is the most likely cause as well, and I would recommend going back to see your dermatologist (or your primary care doctor
) if things are not clearing up.
The most common cause of an allergic or contact reaction in this area would be some personal care product, such as lipstick, that you are using. It would be worth thinking about whether or not a product you might be using could be the cause, since if you continue to use it then things will not likely clear up.
Also, sometimes, these reactions require strong steroid medications to clear up. Desonide is a very weak steroid medication, and your doctor may consider prescribing you a stronger one, although it is important to be very careful about using strong steroids for long periods of time on the skin of the face and the lips.
I also wonder if you might have a component of chapping of the lips, which is mechanical irritation of the lips from moisture, cold, and mechanical damage (such as picking at dry skin). A good chapstick might help with this.
Start by seeing your doctor for a more formal opinion.