Your concern is understandable but try not to stress. I do agree that the issue sounds more dermatological than anything; but since your doctor prescribed an antibiotic it is possible that you have an infection that has never fully cleared. Would you say the skin resembles that of an orange peel? Is the red area fairly red and consistently so? Do you have dimpling of the skin that wasn't there before or a nipple that has become inverted? If the answer is yes, you need to go back to your doctor (which you should do anyway, btw). You are a 16 yr old teenager and the statistical odds of you having breast cancer is roughly 1 in 1,000,000 (literally) - I hope that helps put your mind to rest, but; for your peace of mind you need to follow up with this. You have come on this forum but I, sincerely, hope that you can go to your mom, older sister, aunt, adult friend - someone, to talk to you about this. You shouldn't be carrying your worry without support and having someone able to help you get facts and medical treatment. So, my recommendation (and I am not a doctor) is 1.) Go talk to a trusted adult and get some support 2.) Go back to your doctor 3.) If you have dimpling, redness that doesn't go away, skin that is bumpy resembling an orange peel, or a nipple that has, over time, become inverted or one breast has swelled larger than the other.... then when you talk to your doctor ask (and if need be insist) on seeing a breast specialist.
If your skin is pinkish and flaky I do believe it is a dermatological issue. You might be having a contact dermatitis and would benefit from a antihistamine - that might be worth a try before you head to the doctor but you'll need to give the antihistamine about a week to see if it helps. In the meantime keep the lotion on it. Best of Luck and let us know what you find out!