Nipples are very sensitive and can be painful when irritated.
Jogger's nipple is a common problem for runners, particularly long-distance ones. As you run, your clothing rubs against your nipples and causes soreness, dryness, inflammation and bleeding. This is often much worse if the nipples are erect.
Wearing the right clothing will help to prevent this condition. The best material is silk because it's soft compared with modern synthetic fibres, which can be quite coarse. Loose-fitting sportswear is also good, as it has less opportunity to rub against you. If you need to wear something that fits closely, then Lycra can be less damaging.
Use something to protect your nipples. A plaster is a straightforward idea provided you're brave enough to remove it and some of your chest hairs, too. Surgical tape is available from the pharmacist and works in the same way but is a little less adhesive.
Barrier creams containing zinc, such as those used for a baby's nappy area, are protective and soothing. Many people use petroleum jelly for similar benefits.