Brief Answer:
Acanthosis

Detailed Answer:
I follow your question.

Medications that improve insulin sensitivity, such as metformin and rosiglitazone, may have some benefit for acanthosis nigricans related to insulin resistance. A small 3-month that compared metformin to rosiglitazone in overweight and obese patients with acanthosis nigricans found no significant change in severity of acanthosis, and only modest improvement in skin texture. In another study, subjective improvement in acanthosis nigricans was noted in three out of five adolescents and adults with insulin resistance or diabetes who were treated with metformin for six months. Additional studies are necessary to explore the effectiveness and safety of such medicines in the treatment of acanthosis nigricans.Topical agents, such as topical retinoids, vitamin D analogs, and keratolytics are the primary agents used in the treatment of localized acanthosis such as the type you have under your arms. Topical therapy is impractical for the management of patients with widespread involvement, and treatment options for this population are limited.

So in summary: Data are limited on the treatments for acanthosis nigricans. If an underlying cause is present, treatment or removal of the inciting cause should be attempted, for example: obesity & certain medications; acanthosis nigricans often respond to this form of therapy. The role of agents that improve insulin sensitivity such as metformin in patients with acanthosis nigricans related to insulin resistance remains uncertain.
●For patients who desire accelerated improvement of acanthosis nigricans or in whom treatment of the underlying disorder is not possible or satisfactory, I refer to dermatologists who sometimes suggest a trial of topical tretinoin or a topical vitamin D analog, such as calcipotriol (calcipotriene). Systemic retinoids may lead to clinical improvement in patients with extensive or severe disease, but relapse is common after treatment discontinuation.

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