This looks like a chemical irritation or mild burn from the hair removal cream, especially since it was left on longer than recommended, and the skin under the nose is quite sensitive. The redness, burning, and ongoing irritation usually happen when the skin barrier gets damaged, and applying coconut oil may sometimes trap heat and worsen discomfort in the early stage. Right now, keep the area cool by gently washing with plain water and avoiding any strong soaps, scrubs, or repeated rubbing. Stop using all active products on that area for a few days and avoid makeup or fragrance products until it settles. A simple, bland moisturiser can help, but don't over-apply anything heavy. Since it is on the face and near the nose, it is safer to get it checked if the burning is significant or not improving, as a doctor may prescribe a soothing anti-inflammatory cream suitable for facial skin. Seek medical care sooner if there is blistering, increasing pain, swelling, pus, or if breathing or upper lip movement becomes uncomfortable.

Prickly heat often appears in hot, humid weather, when sweat becomes trapped beneath the skin. It can cause small rashes, burning, irritation, redness, and itching, especially on the neck, chest, back, or in skin folds. Sweating a lot, wearing tight clothes, and staying in the heat too long can make it worse and make your skin more sensitive. Calamine lotion is often used to help soothe the skin and ease irritation and itching over time. Taking cool baths, wearing loose cotton clothes, keeping the air flowing, and avoiding too much sweating can help the rash heal faster. Try not to use heavy, oily creams or wear tight synthetic clothes, as these can block sweat glands and make irritation worse. Staying out of direct heat and changing out of sweaty clothes quickly can also help you feel better while you recover. Usually, the rash gets better slowly with cooling care and by protecting your skin. Consult a doctor if the rash becomes painful, develops pus, spreads quickly, or comes with fever, severe burning, or swelling, since this could mean an infection or another skin problem.

Since your symptoms are seasonal and recurring, it is important to consult a doctor rather than relying solely on over-the-counter treatment. A proper diagnosis helps identify the underlying causes of itching, burning, and rash, ensuring that treatment addresses the root problem rather than just temporarily relieving surface symptoms. Your doctor can determine whether this lotion alone is sufficient or if additional treatments are needed, and may also recommend preventive measures to reduce seasonal recurrence.