Programming is to CS what telescopes are to astronomy. I understand that this is not obvious to an 18 year old outsider, so in that sense you may have been misled by an admissions counsellor who probably didn't understand it either, but no - studying CS won't make you a software engineer by itself. At all.
Unfortunately, in most cases, it's the option you have. An actual software engineering degree concentration would be better for what most people actually want, but it's a rarity. You'd have to entice professors with industry experience (who are good enough to know what they are supposed to teach), and you aren't doing that on typical faculty pay scales.
> An actual software engineering degree concentration would be better for what most people actually want, but it's a rarity.
Part of the problem, IMNSHO, is that we have widespread disagreement with the profession of software 'engineering' (such as it is) about what is mandatory, what is excellent, what is good, what is minimally acceptable and what is intolerable. We even see that what some people think is mandatory others think is intolerable, and vice-versa.
I don't know that we'll be able to have an actual proper software engineering profession for at least another two decades, but honestly closer to a century.