I don't believe that this is a wound. Wounds do not take that long to heal. Look at this website, the wounds are much deeper than ours and they make dramatic improvments with moist treatement within days. http://www.wound-treatment.jp/english/index_e.htm
Some people argue that because we move our lips through eating and talking it takes longer, but if that is the case we should see a dramatic improvement by fasting or only drinking through a straw and applying lip balm constantly for a few days.
Therefore i think it must be an allergy, auto-immune disease, a bacterial, viral or fungal infection, or an inflammatory skin condition like eczema.