A stinging sensation in one or both breasts is most often a hormonal issue. If you're pre-menopausal, hormone levels can fluctuate quite a bit; and this can lead to breast pain, tenderness, soreness, sometimes itching, and stinging. This kind of discomfort is usually more apparent just before your period; so if this stinging sensation has just started, and your period's due, wait a week or so and see if it disappears on its own.
Sometimes, if stinging is happening in just one breast, it might be an early sign of an infection of some kind, such as mastitis. If your breast becomes hot, red, or swollen, or you start to run a fever, then you'd best see a doctor for diagnosis and treatment. But beyond that, it's probably fine to just watch and wait, to see if the stinging goes away on its own.