Is it possible to get a lift and an implant along fixing a inverted nipple?
Correcting inverted nipples at the same time as a breast lift is not wise, as each procedure reduces the blood supply to the nipple area and combining both may be too much reduction to allow the nipple to heal without problems. Although your back problems are probably due to something other than your breasts since the reduction did not correct the problem, it is still probably not a good idea to add an implant that will add weight to your shoulders and neck area. As for wording a claim so that the surgery could be paid by insurance, unless you have something not obvious in the information you supplied, the answer is "no." The breast lift, which is what you need, would be cosmetic.