Engineering is not one of those majors where prestige matters. Engineering is hard everywhere and you will be challenged no matter where you go!
There are rankings of undergraduate engineering, specific for major. For Mech E programs - 1/2 the schools in the top 10 are public flagships (Berkley, Georgia Tech, Michigan, Purdue, UIUC, UT Austin). Usually when people are talking about prestige, these aren’t the schools that come to mind, but these are the engineering powerhouses. All these schools have very strong recruiting, amazing facilities/labs, strong students, etc… The EE rankings look similar.
And then there are the engineering schools without graduate programs that are also very well regarded - Rose Hulman, Harvey Mudd, Olin, Bucknell, Cal Poly SLO, Cooper Union, etc…
If you continue on your current trajectory with grades, rigor, and projected scores, you will be a competitive applicant. However, and this is a biggie, you are OOS for all of the state flagship schools and they all give preference for their instate applicants. You are going to need to figure out a list that includes matches.
You’ve already gotten some good suggestions from other posters. I suggest you start thinking about what matters beyond ranking. Do you want large or small? Urban or rural? Hands on or theoretic learning? Do you want a school with co-ops? Once you have answers to those questions and actual scores, posters here will be able to give you a better sense of schools to consider.
Keep up your hard work!