I had a lumpectomy when I was 15. I was supposed to be awake for the procedure, but something happened and my doctor ended up putting me completely under; I don't remember anything from about 5 seconds after the anesthesia hit until I woke up in the recovery room. I had some mild pain for the first couple days after the surgery, but the worst thing was removing the stitches...and it seems that people are using dissolving ones more and more.
My scar is hardly even visible 14 years later, and I rarely even think about it or notice it. It is less than an inch long...and actually, I don't think anyone who has ever seen my boobs noticed it before I pointed it out.
Try not to worry. At your age, the likelihood of cancer is small...not non-existant, but small. Keep us updated.