Unconstitutional?

Lately I have been going over various firearms laws for New York State, and various other states, and am becoming more frustrated as I read them. As most of you know, the Second Amendment of the Constitution of the United States says that "the right of the people to keep and bear arms shall not be infringed." I am finding that State laws restrict which Americans can "bear arms". According to New York State Law, "No person may carry, possess or transport a handgun in or through the state unless he has a valid New York license. New York does not issue licenses to non-residents nor does it recognize licenses issued by other states." More specifically a US citizen who is also a resident of the State of Nebraska [for example], and holds a concealed carry license to posses and cary a handgun and/or revolver, can not cary or possess a handgun or revolver in the State of New York [for example]. Now, the Fourteenth Amendment of the Constitution of the United States says that "No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States..." So, if the Constitution grants citizens of the United States the right to keep and bear arms, and it also prohibits states from infringing on the rights guaranteed to United States citizens, how can "State A" not allow a licensed handgun owner from "State B" to "bear arms" in "State A"? The Constitution does not limit the arms that the people may keep and bear.
I would really appreciate feedback on this post. Thank you.
~Jim