The phrase helps the reader understand the extremity of the bug bite. By saying that your skin could essentially peel off, shows that with the bite you will have to scratch a lot. The force of scratching could feel like your skin is peeling off. Thus, the bug bite would be very bad and itchy.
For option A, the order of the sentence seems a bit off, the same goes for B and C. I don't have facts to back me up, but if I were to write that, I would go with D. Hope this helps!
