If the above reflects your legal research abilities then its clear why you are having problems. The cases you cited do not say what you claim they do. Did you even bother to read them? Or did you, as I suspect, simply parrot the claim of some web site out there that claims that's what these cases say?
What the U.S. Supreme Court said in the Schware case was very different from what you claim. The issue in the case was not whether the state may require licensing of lawyers. It was instead whether a state may deny a license based on whether the applicant to the bar had been a communist party member. This was, after all, the 1950s and New Mexico, like a lot of the country was caught up in the "red scare" and targeted people merely for being members of the communist party rather than because of any crime they had actually committed. The Supreme Court held that being a communist party member was not a sufficient reason to bar admission to the bar. It stated:
A State cannot exclude a person from the practice of law or from any other occupation in a manner or for reasons that contravene the Due Process or Equal Protection Clause of the Fourteenth Amendment. Dent v. State of West Virginia, 129 U.S. 114, 9 S.Ct. 231, 32 L.Ed. 623. Cf. Slochower v. Board of Higher Education, 350 U.S. 551, 76 S.Ct. 637, 100 L.Ed. 692; Wieman v. Updegraff, 344 U.S. 183, 73 S.Ct. 215, 97 L.Ed. 216. And see Ex parte Secombe, 19 How. 9, 13, 15 L.Ed. 565. A State can require high standards of qualification, such as good moral character or proficiency in its law, before it admits an applicant to the bar, but any qualification must have a rational connection with the applicant's fitness or capacity to practice law. Douglas v. Noble, 261 U.S. 165, 43 S.Ct. 303, 67 L.Ed. 590; Cummings v. State of Missouri, 4 Wall. 277, 319—320, 18 L.Ed. 356. Cf. Nebbia v. People of State of New York, 291 U.S. 502, 54 S.Ct. 505, 78 L.Ed. 940. Obviously an applicant could not be excluded merely because he was a Republican or a Negro or a member of a particular church.
Schware v. Bd. of Bar Exam. of State of N.M., 353 U.S. 232, 238–39, 77 S. Ct. 752, 756, 1 L. Ed. 2d 796 (1957)(Bolding added). You can see from the sentence that I put in bold that the Court did not object to state requiring that lawyers be licensed by the state. It specifically said that the state can require high standards for admission to the bar — and admission to the bar is the granting of the license to practice law. Indeed, the Supreme Court itself requires that lawyers appearing before it be members of the bar of that court, and one of the requirements for admission to the Supreme Court is that the lawyer is admitted to the bar of his/her state and in good standing.
So, the Court saying that a state cannot refuse to license someone because he is a communist party member is quite different from what you claimed the court said. The court nowhere said that a state may not require those who practice law to have a license. Instead, the statement I put in bold says just the opposite.
Your citation of the Sims v. Aherns case is even worse. That case had nothing at all to do with licensing of any profession, let alone lawyers. The issue in that case was whether the new state income tax violated the state constitution. The Alabama Supreme Court said it did. The State fixed that problem by amending the state constitution to add Amendment 25 to specifically allow for an income tax.
If you can't be bothered to read the cases you cite and analyze them properly for what the actual holding of the case is then you are going to fare badly in court. You'd need to do much better than what you did with the two cases you cited above. You weren't even close on either one.