Traditionally, you are correct. But nothing matters anymore, so
The doctrine of the right to travel actually encompasses three separate rights, of which two have been notable for the uncertainty of their textual support. The first is the right of a citizen to move freely between states, a right venerable for its longevity, but still lacking a clear doctrinal basis.
I don’t think the states are allowed to prohibit interstate travel
Traditionally, you are correct. But nothing matters anymore, so
https://constitution.findlaw.com/amendment14/annotation11.html