what branch of gov. is in charge of directing taxes,

and if health care changes, will taxes be raised

The legislative branch has the power to raise money for government services, i.e. taxes.

We have no idea how (or even if) health care will change. Many different plans have been proposed, but undoubtedly if the U.S. provides health care for everyone, taxes will be raised. The question will be whether the bulk of the taxes will be assessed to businesses or to individuals. Some has to pay for health care.