Here's some information I found when searching for Antibiotics and peeling skin:

"What could be the cause of of skin peeling after Antibiotic treatment?

Skin infections are commonly caused by bacterial living on the skin including Staphylococcus. Some species of Staphylococcus produce toxins that can cause skin peeling as part of the infection and inflammatory process. Infections with Stahylococcus aureus can cause Staphylococcus Scalded Skin Syndrome due to the exfoliative toxin the bacteria produces."
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"If you ACIDIFY your skin (find safer alternative to GENTIAN VIOLET), staph bacteria can't grow there."

"Staphylococci can be found normally in the nose and on the skin (and less commonly in other body locations) of 25%-30% of healthy adults. In the majority of cases, the bacteria do not cause disease. However, damage to the skin or other injury may allow the bacteria to overcome the natural protective mechanisms of the body, leading to infection. Staph infections of the skin can progress to impetigo (a crusting of the skin) or cellulitis (inflammation of the connective tissue under the skin, leading to swelling and redness of the area)."

"Scalded skin syndrome is a potentially serious side effect of infection with Staph bacteria that produce a specific protein which loosens the "cement" holding the various layers of the skin together. This allows sloughing of the top layer of skin."

White gunk???= "Of importance is the sticky-looking substance woven between the round cocci bacteria, which is composed of polysaccharides and is known as “biofilm.” This biofilm has been found to protect the bacteria that secrete the substance from attacks by antimicrobial agents such as Antibiotics , resulting in methicillin-resistant Staphylococcus aureus, or MRSA."

"Antibiotic-Resistant Staph aureus is often associated with recent Antibiotic use."

The diagnosis of SSSS is made clinically. This is sometimes confirmed by isolation of S. aureus from blood, mucous membranes, or skin biopsy; however, these are often negative. Skin biopsy may show separation of the superficial layer of the epidermis, differentiating SSSS from TEN, wherein the epidermal-dermal layer is separated in the latter. SSSS may be difficult to distinguish from toxic epidermal necrolysis and pustular psoriasis.

Minor skin infections are usually treated with an Antibiotic ointment such as a nonprescription triple-antibiotic mixture. More serious infections are treated with Antibiotics through a vein (intravenously). Most strains of S. aureus implicated in SSSS have penicillinases, and are therefore penicillin resistant. Therefore, treatment with Nafcillin, oxacillin, or vancomycin is typically indicated. Clindamycin is sometimes also used because of its inhibition of exotoxins.