My nipples became puffy but there's not hard tissue underneath.

Thank you for sharing your question.  It sounds as if you may a condition termed pseudogynecomastia - an abnormal accumulation of only adipose tissue and not gland.  This can often be treated by liposuction alone, or you can return to working out.  Hope this helps.

It's difficult to say without examining you. The swelling could be related to gynecomastia. Gynecomastia doesn't always have hard tissue under the nipple. Some gynecomastia is mostly fat and will therefore be softer. If your concern contact your primary care doctor for an examination.

Ones is the accumulation of fatty tissue the other is glandular breast tissue. Try and go back to the gym and lose some weight. If it improves its likely fatty tissue if not or it actually gets worse it maybe glandular tissue and you will need an evaluation to the cause of it. If its painful seek the advice of a doctor as soon as possible.Good luck!

Gynecomastia does not always entail hard tissue. Often, it is excess fat like you described. Obviously, if the condition improves with exercise then my recommendation would be to get back to working out. It's a lot simpler than surgery. Best of luck.

From your description it may be gynecomastia.You should be examined by an experienced  Gynecomastia   surgeon to discuss your case.