All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
Commercial health insurance is prohibited as previously underlined in Fataawa 82599 and 81425.
However, your work as a programmer designing a telephone system that gathers information about clients and transmits them to the businesses and service providers in order to fulfill the clients' lawful requests, some of these clients being insured by Medicare, has nothing to do with the prohibited commercial insurance contract. So there is no harm in you designing this program.
Allaah Knows best.