Note that even without the 11th Amendment, a state cannot be sued in federal court by one of its own citizens, because Article III, Section 2, Clause 1, does not give the federal courts the jurisdiction to entertain such suits.
With the exception of Virginia, every state has waived sovereign immunity. This means that Virginia is the only state which cannot be sued by its own citizens, or by citizens of the other states.
There are innumerable court decisions published in the law books pertaining to this.
Here is Article III, Section 2, Clause 1:
The judicial Power shall extend to all Cases, in Law and Equity, arising under this Constitution, the Laws of the United States, and Treaties made, or which shall be made, under their Authority;--to all Cases affecting Ambassadors, other public Ministers and Consuls;--to all Cases of admiralty and maritime Jurisdiction;--to Controversies to which the United States shall be a Party;--to Controversies between two or more States;--between a State and Citizens of another State;--between Citizens of different States, --between Citizens of the same State claiming Lands under Grants of different States, and between a State, or the Citizens thereof, and foreign States, Citizens or Subjects.
The eleventh amendment to the Constitution of the United States was proposed to the legislatures of the several States by the Third Congress, on the 4th of March 1794; and was declared in a message from the President to Congress, dated the 8th of January, 1798, to have been ratified by the legislatures of three-fourths of the States. The dates of ratification were: New York, March 27, 1794; Rhode Island, March 31, 1794; Connecticut, May 8, 1794; New Hampshire, June 16, 1794; Massachusetts, June 26, 1794; Vermont, between October 9, 1794 and November 9, 1794; Virginia, November 18, 1794; Georgia, November 29, 1794; Kentucky, December 7, 1794; Maryland, December 26, 1794; Delaware, January 23, 1795; North Carolina, February 7, 1795.
Ratification was completed on February 7, 1795.
The amendment was subsequently ratified by South Carolina on December 4, 1797. New Jersey and Pennsylvania did not take action on the amendment.