In a pickle.... Does graduate school matter for Chem E, & should I apply to prestigious schools?

You mean this? “Employers that cares college names won’t see nameless BS to Ivy MS as good as just Ivy BS.”

There are some employers who would only hire from a set of well known top colleges. If your BS is not one of them, but your MS is, then you might get an interview from those employers due to your MS degree.

HOWEVER, such employer might still look down on you due to your BS degree, even though you earned MS afterward from a top college they do hire, during the hiring process.

MS is often just not a big deal and there is no reason to go for it except some special occasion, such as being able to get BS+MS in 4 years using AP & CC credits, or if it is funded (rare) or there is good scholarship (also rare). MS is often full pay even for those who would qualify need based scholarship for BS, so you would be adding 1~2 years of debt instead of income for not much benefit (unless you couldn’t find employment with your BS)

As you can see, MS is a revenue earning program for colleges and admission is much much easier than BS at the same competitive colleges, unlike funded Ph.D. at the same colleges that is even harder than BS. And employers know this, obviously.

Anyway, that is only until you get hired. Once you are in, then only your job performance will matter.

By the way, Ph.D is a big deal. If you get a Ph.D, then it doesn’t matter where you got your BS, and your starting pay and promotion prospect could be much better than BS, if you get a job that does want Ph.D.