Will an aerola reduction work for me? I have really big puffy nipples and I hate them.

Hello, areola reduction surgery is usually an effective way to decrease the size of the areolae.  It is not common for them to stretch back to their original size, although depending on the technique and whether implants  are inserted at the same time, this is a potential risk.  The operation results in scars around the areolae and possibly on the breast mound as well.   If you arrange a consultation with a plastic surgeon they can discuss the different options in more detail.

You do appear to be a good candidate for areolar reduction. This could be done with a small light to position the nipples in a better position as well. The areola can stretch afterwards but there are techniques to decrease the risk of this. 
See a board certified plastic surgeon for a consultation to get a better idea of what you can expect. 

Based on these photos you seem to be a good candidate for peri-areolar (doughnut) breast lift. It will allow reduction of areola size and create some lift of the breast. Better result would be possible with lollypop type of lift but it will create more scar. It is also possible to do reduction of areola only. In person evaluation and discussion about your goals and expectations would help. Good luck.

Thank you for the question.
Areola reduction  involves  circumferentially removing areola  skin  around a smaller areola design. This procedure can be done under local or general anesthesia. It is often  done as part of a breast augmentation/lift,  breast lift or breast reduction  procedure. If the areola are "puffy" (for example, as seen with constricted or tuberous breasts) some breast tissue excision may be helpful.
Patients should be aware that despite best efforts scarring will be visible and potentially abnormal ( possibly thick, raised and/or pigmented).  Some areola  asymmetry may also  be present after surgery.  Their is a small chance that  a patient may lose sensation.
As with all plastic surgical procedures, patients must weigh the potential benefits against the potential risks/complications while making decisions.
I hope this helps.