There could be several reasons you might feel a burning sensation in your nose after exercising, but outside influences are ultimately the cause for most of them. In that case, controlling your environment while exercising is the best way to prevent the symptom. Contact your doctor if the burning persists or is severe.
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Some medications that treat allergic rhinitis, or seasonal allergies, can cause a burning sensation in the nose. If you take an antihistamine before exercising outdoors in order to prevent allergy symptoms, the burning sensation may show up during or shortly after your workout. Talk to your doctor about switching to a different medication that doesn't have burning nose as a side effect.
When you inhale, tiny particles in the air get in your nose. Most of these particles are harmless, but those generated by pollution can cause burning in the nose, eyes and throat. Check your city's air quality and pollution indices; if pollution levels are high in your area, exercise indoors or time your workouts for times of day when pollution levels tend to be lower, such as early morning or late evening.
If the burning sensation is occurring in your chest as well as your nose, along with a tight feeling in your chest, you may not be breathing deeply enough to get adequate oxygen to your lungs. This could be due to a condition referred to by the Mayo Clinic as exercise-induced asthma, or asthma that's only triggered by strenuous activity. Short-term inhalers and/or long-term asthma medications can help control this condition.
Dry air can irritate fibers and blood vessels on the inside of your nose, causing a burning sensation or even nosebleeds. Dry air often occurs during winter and in low-humidity climates. If you exercise outdoors, choose days on which the humidity level is higher. Indoor environments can contain dry air as well, especially if the heating or air conditioning is turned on. Use a humidifier and limit your use of climate-control devices when exercising indoors.