I have implants placed by a transaxillary incision. Is it possible to have them removed and replaced a different way? (Photo)

In my opinion it is a must to approach your breast revision through a different incision. Inframammary would be the choice incision. Although transax approach is still available, it has fallen out of favor for variety of reasons. Approaching your breast via an inframammary approach will allow correction of your bottomed out implants by tightening of the lower pole and capsule of your breasts. Good luck.

Absolutely.  In my opinion, it is much preferable to remove and replace breast implants  through an infraareolar or inframammary approach.  In my practice I would likely recommend an infra areolar incision in your case; I would also recommend adjustment of the breast implant capsules to improve positioning of the breast implants given that one of your implants seems to be sitting too low (and a little too far medially) compared to the other side.   In other words, careful planning and careful execution of the procedure should result in improved symmetry of your breasts. My best advice: select your plastic surgeon carefully. Make sure that he/she has significant experience achieving the types of outcomes you will be pleased with. Then, communicate your goals carefully, as well. Working together you will come up with a good plan to achieve your goals.  
Best wishes.