I can understand that seeing skin peeling from your nipple must have caused you some concern.
It would be very unlikely to be anything serious such as cancer. We can't diagnose (tell you what's wrong) and we always advise anyone who is worried about any new symptom to get checked out by their doctor.
Nipples can be very sensitive. You may find that you may have an allergy or sensitivity to either some soap, washing powder or any lotion that you may have applied. You may also have some skin irritation through wearing a lacy bra but of course I can't be sure. The charity Breast Cancer Now have some information about what breasts should feel like which you can see here
If it does not seem to be settling down then do make an appointment with your GP. They may be able to prescribe you some cream to help moisturise the skin and prevent any further peeling.
You may want to try and use a gentle soap like simple and make sure that you dry the nipple well.
If you feel that it would be helpful, do share this with a trusted adult or your mum if you can.
