I don’t think so-The 11th protects the States from lawsuits—not individuals.
Eleventh Amendment | United States Constitution | Britannica
https://www.britannica.com/topic/Eleventh-Amendment
The Eleventh Amendment, amendment (1795) to the Constitution of the United States establishing the principle of state sovereign immunity.
Under the authority of this amendment, the states are shielded from suits brought by citizens of other states or foreign countries.
It is, for all intents and purposes the first amendment that sought to correct or at least clarify a seemingly concrete element of the Constitution. In Article III, Section 2, the federal judiciary is given authority to decide “Controversies…between a State and Citizens of another State.”
Although it was presumed (wrongly) that the doctrine of sovereign immunity was clearly understood to preclude such actions, the U.S. Supreme Court in Chisholm v. Georgia (1793) permitted a suit brought by a citizen of South Carolina against the state of Georgia.
Fearing that other states would follow suit, the amendment was proposed on March 4, 1794. It was ratified by 12 of the then 15 states on Feb. 7, 1795.