Any hospital or institution securing a lien under this chapter may enforce its lien in a civil action against the tort-feasor, the insurer of the tort-feasor, or the insurer of the injured person. A judgment obtained against the tort-feasor or any insurer does not bar the hospital or institution from collecting the amount of its account from the person for whom the services were rendered, or that person’s insurer, unless payment has been made by the tort-feasor or tort-feasor’s insurer to the hospital, and then only to the extent that payment has been made.