The cause of sore nipples and prolonged feeding by the baby is due to improper feeding technique . When the baby sucks at only the nipple she gets only a small amount of milk and leaves your nipple sore . There is proper positioning technique while feeding so that when the baby is sucking the complete nipple and almost whole of the upper areoala is in her mouth. Only that will ensure adequate pumping action of milk from the breast . Switching to formula milk is an easy job but why should you deprive the baby of the goodness of mother's milk . Moreover once you start once or twice formula feeding , many times baby starts preferring formula milk over breast milk as mechanism of both types of feeds is different . In your case it just requires a simple adjustment of positioning technique and that will solve the problem Lot of lmage and video resources about this are available on the internet ,  or you may seek the advice of a Pediatrician regarding the same