Thanks for the query. This presentation can be seen with many skin diseases. The best option is to consult a Dermatologist in person to understand the problem and get it diagnosed. A proper treatment can then be started. Discuss the situation and hope it will be cleared in few days. Don't delay the appointment. You can use a bland moisturiser till then and OTC anti-allergic medications.Don't worry it will resolve for sure if you correctly follow the recommendations.
Kindly consult a dermatologist for exact diagnosis and a precise treatment plan.
Greetings. Under arms usually are sites which are protected from sun exposure unless you have been actually lying down under the sun with arms raised!! So unlikely that its a tan. Now pigmentation there could be due to acanthosis nigricans or pigmented dermatitis due to use of perfume / deodorant... See a qualified dermatologist near you. Warm regards