I do not believe that is correct. There was at least one state decision that cited the Second Amendment. Shall not be infringed is much more inclusive than "Congress shall make no law".
It was only after the 1830's when the Supreme Court ruled the Bill of Rights did not apply to the states, that infringements on Second Amendment rights started being upheld in the State courts.
It was true of the second amendment as well as state supported religions. Nor was there freedom of speech and assembly with regard to the South.
Article I, Sections 9 and 10.
Barron v Baltimore was the first BoR case before the Court in 1833. And the Court found (unanimously) that the prohibitions in the BoRs were inoperative unless the Constitution expressly made the states subject to the prohibitions.
The third clause (of Section 9), for example, declares that “no bill of attainder or ex post facto law shall be passed.” No language can be more general; yet the demonstration is complete that it applies solely to the government of the United States.... the succeeding section, the avowed purpose of which is to restrain state legislation... declares that “no state shall pass any bill of attainder or ex post facto law.” This provision, then, of the ninth section, however comprehensive its language, contains no restriction on state legislation.