You have darker skin so that patch on your upper lip which is still black IS your true lip colour is it not?
You say the bottom lip does not peel, that is the normal colour? It looks as though is does peel.
I'm sorry to say this but I think you'd be better off leaving them alone + moisture. You are a prime candidate for daniel miller's aquafor moisture method.
Soaking and gentle exfoliation ( Epsom Salt baths) is the last thing you want IMO. The many differential with your lips is I don't note much redness/inflammation.. if you see my blog there is clearly redness on the inside of the mouth which you don't have.