Wow, this is terrifying.

Article IV, Section 2, Clause 1:

The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.

The Supreme Court has long recognized the right to travel from one state to another under the Privileges and Immunities Clause,1 as well as other constitutional provisions.2 For example, the Court held that a state could not constitutionally limit access to medical care to its own residents, and deny access to nonresidents, without interfering with the right to travel.3
In Saenz v. Roe, the Court characterized the constitutional right to travel as having at least three different components:

It protects [1] the right of a citizen of one State to enter and to leave another State, [2] the right to be treated as a welcome visitor rather than an unfriendly alien when temporarily present in the second State, and, [3] for those travelers who elect to become permanent residents, the right to be treated like other citizens of that State.4
While the Court did not expressly identify the constitutional basis of the first component, it noted that the Articles of Confederation’s privileges and immunities clause explicitly protected the free ingress and regress to and from any other State.5 As for the second component of the right to travel, the Court found it to be expressly protected by the text of the Constitution through the Privileges and Immunities Clause.6 Saenz connected the third component of the right to travel to the Fourteenth Amendment’s Privileges or Immunities Clause.7
constitution.congress.gov/browse/essay/artIV-S2-C1-13/ALDE_00013789/%5b%27travel%27%5d