You will file a non resident IL tax return and pay IL income tax only on the income you earned while physically present in IL.
Q. Does idea of buying an apartment in Chicago make my IL state tax situation more unfavorable?
A. No, in my opinion; but possibly. State tax agencies can be aggressive with "residents" who have 2nd homes in non-taxing states (e.g. TX). But your TX home appears to still qualify as your "domicile".
References:
https://www2.illinois.gov/rev/questionsandanswers/Pages/369.aspx
Which says, in part, "You are an Illinois resident if you were domiciled in Illinois for the entire year. Your domicile is the place where you reside and the place where you intend to return after temporary absences."
and https://www.isba.org/sections/statelocaltax/newsletter/2010/06/imanonresidentofillinoismaybe
Which says, in part, "A resident of Illinois is usually, but not always, domiciled in Illinois. The term “domicile” commonly means an individual’s 'permanent home,' which is where the individual intends to return to after a period of absence. A person has only one domicile and does not acquire a new domicile without first abandoning the prior domicile."
