If you’re a Texas resident eligible for in-state rates, then UT-Austin may very well be the school to beat for a mechanical engineering major.
Cornell, UPenn, Northwestern, JHU, Harvey Mudd, Rice … Tufts, USC … are all more selective than your in-state public options, but not as selective as Harvard, Stanford, or MIT. FWIW, they also have higher overall USNWR rankings than UT Austin. For a family earning ~$90K/year, they may be competitive for net price with UT Austin.
Whether they all have mechanical engineering programs as strong as UT Austin’s, I don’t know.
USNWR does rank undergraduate engineering programs (based solely on “peer assessment” surveys).
It ranks UT-Austin #10 for undergraduate engineering (in general) and #10 for mechanical among PhD-granting universities. Cornell is tied for #10 (in general) and is #8 for mechanical. USNWR ranks Harvey Mudd #1 for engineering (in general) among schools that do not grant PhDs. The other schools I suggested all have lower USNWR engineering rankings than UT Austin. How you weigh that in your list-building is up to you. I think differences of a few ranking positions (maybe even 10-20 positions) are insignificant.
If your objective is to build a more balanced list (in terms of admission selectivity), but only with schools ranked about as high or higher than UT-Austin for engineering, then your options are very limited (since UT-Austin is ranked so high). Schools that satisfy those criteria are Berkeley, Georgia Tech, UIUC, Michigan, and Purdue. However, it doesn’t make much sense to pay a large OOS price premium just for a slightly higher peer assessment in engineering. In my opinion, it may make sense to pay a small price premium (or possibly even a lower price) for a more selective, higher-ranked school (even though its engineering ranking is a little lower). It just depends on your criteria and goals.
Some of the comments above are harsh but they are on the money. Unless your high school is the top high school in Texas and has average SAT scores of say 2000 or ACT above 30, you are simply not a strong candidate for schools like Stanford and would be wasting your $90. An unweighted GPA of 3.8 is not bad but applicants to these top schools fare much better with 3.9 or 4.0 GPAs. It is really not a good idea to disclose your struggle with depression. How would that possibly strengthen your application?
Don’t attract attention to a minor problem (9th grade results) and do not mention depression, which colleges tend to worry about, causing you to lose if there’s a toss up between you and someone without depression. If it is brought up at all, it should be by your GC, and only in terms of how hard you’ve worked and are now recovered. (If you’re admitted, register with health services etc.)
UT is a great school but right now it’s not a safety since you’re outside the Top 8% threshold. In addition, even being inside the 8%, doesn’t guarantee you’ll get MechE.
UTD is a good safety pick for its Honors program and McDermott is a great program.
However it’s a bit short.
Harvard, Stanford, etc., are not going to happen. Your academics are on par with what they want, but your EC’s arent.
As a girl, you’d have a shot at Olin - an excellent engineering college near Boston.
Smith would probably be another match. Agnes Scott, with its partnership with GATech, may be attractive, even if I’m not sure how FA would work for the last years of the program. For that reason, and because you have the stats, you should go with Smith.
Look into UAlabama’s College of Engineering: it’s pretty good, near research park (=internships), and you’d automatically get Honors College, Honors Dorm, and a full tuition scholarship plus a stipend.
I would NOT bring up depression in your application, even if you feel it would make a good story or explain some bad grades. Depression is a HUGE red flag to colleges, especially top tier colleges that are facing problems with students committing suicide.