No STD causes th sort of burning sensation or skin 'drying' that you describe. You probably have a fungal infection (jock itch) or some other garden-variety skin condition. Try keeping the area clean with soap and water, and perhaps try an over the counter antifungal cream, such as Lamisil; you will find such products on the same shelves as products for athlete's foot.
Clear mucus from the penis is normal after sexual arousal or ejaculation. It has nothing to do with your skin problem.
If cleaning and the antifungal cream don't clear up your skin symptoms, see a health care provider. There is nothing to be embarrassed about.
HHH, MD