Will my breasts stay cone shaped/pointy with puffy areolas after surgery? (photos)

The choice of implant and the technique used to place the
implant has a lot to do with the final shape of the breast. Giving your
pictures, I would suggest you consider a round moderate profile implants placed
over the muscle. This will contribute to the roundness of your breast without
promoting more cone shape. Your recovery will be easier than under the muscle
and you will not have animation deformity from the muscle flexing and twitching
the breast.
 

Usually the breast will stretch due to the implant, initially it will be firm and somewhat tight but then it tends to soften, feel softer and look more natural once again (unless you choose excessively large implants).  As part of this stretching and softening process the shape tends to change and the conical shaped breast will become more rounded, particularly in the lower breast.You're breasts are symmetrical and very natural in appearance and therefore you are likely to have an excellent result with most methods of augmentation you and your surgeon choose.All the best,Dean

Hi. The answer to your question is twofold. The shape of your breast will become softer and more rounded with a round implant. A teardrop will tend to be more conical. Your areolae are normal. However the 'puffiness' will be bigger and more noticable postop.  If you want more lower pole fullness then a dual plane 2 should be used. 
Regards
Damien