Hi pmelol,
Sorry to hear about your nipple issue. It's very difficult to tell you whether it is gyne just by the images you posted. A doctor would need to do blood work on you to check hormone levels and a physical exam to rule out serious medical conditions and to assess whether it is gynecomastia.
See this link about the side effects of finasteride:
Finasteride Side Effects in Detail - Drugs.com. One of the less common side effects is indeed breast development/enlargement. If the issue is in your nipples alone, you should see a doctor as soon as possible for an exam, just to be safe. If you have had (or begin to experience) any discharge from the nipples, see a doctor right away.
If you are seeing breast fat development, you might try losing a little weight, say 10 pounds, and see if breast size reduces at all. If not, see a doctor to confirm or deny gyne.
If you're going to be in the NY area anytime soon, feel free to make an appointment at either of my offices in Manhattan or Long Island. You can call (631) 499-1831 to schedule. I am a Board Certified Internist as well as a gynecomastia specialist & cosmetic surgeon, so I'd be happy to examine you at no charge and advise you on your best next steps. You can also visit my website here:
Gynecomastia Surgeon New York City & Long Island - Male Breast Liposuction
All the Best,
Dr. A