**Core Concept**
The question is testing the understanding of adverse drug reactions, specifically those related to **antibiotics** and their effects on the skin. The scenario describes a condition following the administration of Co-trimoxazole, an antibiotic.

**Why the Correct Answer is Right**
The description of extensive peeling of the skin without mucosal lesions or toxicity in a patient treated with Co-trimoxazole suggests a condition known as **Stevens-Johnson Syndrome (SJS)** or more likely, given the lack of mucosal involvement and the specific context, **Toxic Epidermal Necrolysis (TEN)**, although the latter is more severe and less likely without mention of mucosal lesions. However, another condition to consider given the specifics (especially the age and the drug) is **erythema multiforme**, but the key here is the mention of "extensive peeling" which points towards a more severe reaction like TEN or a similar condition specific to the context provided.

**Why Each Wrong Option is Incorrect**
**Option A:** This choice is not provided, so we cannot assess its accuracy.
**Option B:** Without the specific details of option B, it's challenging to determine why it's incorrect, but given the context, if it doesn't align with a severe skin reaction due to Co-trimoxazole, it would be incorrect.
**Option C:** Similarly, without specifics, if this option does not describe a condition consistent with a severe drug reaction leading to skin peeling, it would not be correct.
**Option D:** Again, lacking the details of option D, if it doesn't match the clinical presentation described, it's incorrect.

**Clinical Pearl / High-Yield Fact**
It's crucial to recognize that certain medications, including antibiotics like Co-trimoxazole, can cause severe skin reactions. The absence of mucosal lesions and systemic toxicity might lean the diagnosis away from conditions like Stevens-Johnson Syndrome, but the presence of extensive skin peeling is a red flag for a severe drug reaction.

**Correct Answer:** Correct Answer: D. Toxic Epidermal Necrolysis.