How does the professional class fit into Marx and Engel's class struggle theory?
Marx's discussed struggle had less to do with your income-position in society and more to do with how you derive income, whether through profits, wages, or rents. You bring up a fascinating issue with his analysis and the solution is all about framing. Even doctors end up selling their labor on the market (in increasingly specialized components). While the labor of a doctor is different than say a machinist, their income is fundamentally different than that of someone who owns the means of production. The 17th century putting- out system would be maybe the clearest split between the two.  Keep reading Marx! Eric Fromm has some great essays that explain the nuance in Marx's world view. Hopefully this answer helps