I'm 18 years old and very insecure about my breasts. My areolas are big and 'puffy' Why are they puffy?

From your photos, it's possible that your breasts could be tuberous or that you just have a large areola. Unfortunately this is not something that could be fixed without surgery. It's not abnormal - it's just that breasts come in all different shapes and sizes. If you were interested in surgery, this would involve a reduction of the areola. 

Thank you for sharing your question and photographs.  Your "puffy" nipples is a common variant in the spectrum of breast appearance but can also be associated with tuberous breasts.  This can not be appropriately evaluated in your supplied pictures.  That said improvement can be accomplished but requires surgery.  See an ASPS board certified plastic surgeon in consultation to discuss.