Puffy or pointed nipples could be caused by a number of factors. When referring to puffy nipples, you are more likely to be talking about the entire areola area of the breast or male chest. An excess in fat or glandular tissue can cause swelling of the area which gives the puffy appearance. Conditions such as gynecomastia and tuberous breasts can cause the appearance of puffy or pointed nipples in men and women. Find out more about Gynecomastia treatment here.Find out more about Tuberous Breast Correction here. Large nipples can also cause the appearance of a puffy or pointed nipple in men or women. Nipple reduction surgery can help to reduce the size of the nipple so that it is more in proportion to the rest of your chest or breast. Find out more about nipple reduction surgery here.