Gynecomastia male breast reduction
Even with minimal breast tissue enlargement, an enlarged areolar diameter tends to produce a feminized breast/chest appearance. For patients with an enlarged areolar diameter, an areolar reduction can be performed in addition to direct excision of breast tissue and liposuction. This requires an incision, and thus a scar, that encompasses the entire circumference of the areola. However, the scar is usually obscured fairly well by the color difference between areolar skin and the adjacent chest skin, and the reduced areolar diameter can be critical to producing a more masculine appearance of the anterior chest.
You can have the excess tissue removed to make your nipples less puffy, but with any surgery you will be left with a minor scar. Please see a surgeon who is experienced in this.
Puffy Nipples, Not Gynecomastia
You need to be examined by a surgeon or have some photos to be reviewed. Seek a plastic surgeon with specialty training in gynecomastia surgery.
Puffy Nipple Is Gynecomastia
One type of gynecomastia is referred to as "puffy nipples." This is when the excess tissue (typically gland) is confined to the borders of the areola. This will show more with contraction of the pectoralis or when your areolas are warm (after a hot shower), but will look better when stimulating the nipples or when they are cold. I recommend being evaluated by a plastic surgeon who is experienced in evaluating gynecomastia patients.
You are describing a very mild form of gynecomastia
You are describing a very mild form of gyenecomastia. When confined to the areaola, a reduction in the size of the areola and resection of the tissues just deep to its surface is usually sufficient to remedy the situation.
Gynecomastia cause of puffy nipples
Puffy nipples is usually a result of excess glandular tissue, which is a condition called gynecomastia. This can be corrected by removing the excess tissue, as well as possibly reducing the size of the areola.
Pictures would be helpful, but it sounds like you may have a mild form of gynecomastia. If the appearance is bothersome, a simple subareolar resection will recontour the tissues beneath the areola and masculinize your chest contour. Sometimes liposuction will be used to feather out the resected area. Consult in person with an experienced plastic surgeon.
Puffy nipples (areola)
What you describe is gynecomastia. Feeling it is different than seeing it. If it is visible, then it may make sense to have it surgically excised. If it is just palpable, it may make sense to observe unless it really, really bothers you. Procedure is rather easy and includes a well camouflaged incision around the areola. Recovery is quick.
Gynecomastia is usually caused by a combination of excess fat and breast tissue. In some patients with little body fat, it is the breast tissue causing the result. Fat can be removed with specialized liposuction techniques ( that also help skin to contract), while the excess breast tissue needs to be excised through a small incision around the areola.
Hope that helps.
Gynecomastia can be large of small
Even though your case may be mild, it sounds like it is bothersome to you. It is true that even men have breast tissue, but if it is palpable and annoying to you, (in my opinion) it is worth removing if its affecting your quality of life.