Where to apply, what are my chances?

Hello. I was wondering if anyone would be willing to give me a gauge as to where I should apply and what my chances would be for getting in.

Background:
I’m a white female from New Jersey who would like to go into physical science. My school doesn’t report rankings but I know that I’m somewhere in the top 5-ish% of my class. I’m a junior.
Note: I have struggled with my mental health since I was young due to a complicated childhood. It was particularly bad during my freshman and sophomore years (which is important to understand regarding my academics and ECs).

Academics:
1550 SAT (I’ve only taken it once, so I’m going to try to improve): 770 reading, 780 math. I also plan on taking Math 1, Math 2, and Chemistry.
As previously mentioned, I struggled with severe mental health issues especially freshman year, which resulted in me getting a 504 plan. My grades were terrible for a while but I was given permission to complete some earlier assignments at the end of the year and eked by with a 4.1 weighted GPA by the end. Since then, I’ve managed to bring up my GPA to a 4.324 and am averaging a 4.7 each quarter. I will have approximately a 4.4 by the end of first quarter of my senior year. I got a 5 on the AP World History exam last year. I skipped precalculus at school by taking a 5-week course at the local community college and received an A. I’m currently taking AP Chemistry, AP Calculus AB, AP Lang & Comp, and APUSH and averaging A’s.

*Extracurriculars:
I am vice president of the French chapter of my school’s World Language Honor Society. I’m also in the Science National Honor Society and National English Honor Society. I’m in my school’s yearbook club and am guaranteed a leadership position next year. I’m also in my school’s Leo’s club. I plan on working at a local math tutoring place this summer and next year. I was in an audition-only wind ensemble freshman and sophomore year but had to quit this year due to scheduling issues. I’m currently in a concert band outside of school that is affiliated with a well-to-do private school in the area. I have been taking private flute lessons since seventh grade and have played since I was 9. I volunteer at a food pantry every Saturday.
*Because of my extenuating circumstances, I wasn’t really able to get involved in clubs until the end of sophomore.

My parents both went to a local college and don’t know much about the college admissions process, so I would really appreciate literally any advice you could give me. Thank you for your time!

Which of the physical sciences are you interested in?
Do you need financial aid?
What is your unweighted GPA?
What year did you have the problems with GPA? Was it grade 9? or 10?
Are you going to divulge the mental health issues in your application?

Some other info that will help people make recommendations, in addition to @sgopal2 questions:
Do you have any idea of whether you will prefer an urban, suburban or rural environment?
Will you prefer to be in a certain part of the country, or a certain distance from home?
Will the size of college matter to you? you can find schools from hundreds or students, to tens of thousands.

I do not plan to apply for financial aid, I would prefer an urban/suburban environment, I’m leaning towards physics, I would prefer a medium-to-large sized school, I don’t particularly care about its geographic location, I’m not sure of my unweighted GPA but if I had to guess it’s somewhere in the 3.8 to 3.9 range, and I do intend on disclosing that information on my application.

Your stats and scores are excellent. 3.8-3.9 is pretty darn good, even with a downswing. So whatever happened earlier on in high school, it doesn’t seem have impacted you much.

Here are some suggestions for colleges:

Reach: Caltech, MIT, UChicago, Princeton
Match: Stevens, Harvey Mudd, Pitt
Safety: NJIT, Rutgers, Drexel

Wanted to add some more details. For the reach colleges, it is difficult for anyone to get accepted, even those with perfect scores. Your stats are definitely within range. So it will come down to whether or not the adcom wants you. They try to balance genders, geography and other factors. You don’t have any ‘hooks’ which typically can help. So a lot of it comes down to random factors on whether you are accepted or not.

The best thing you can do to increase your chances is to apply binding early program. Of the colleges I listed in reach, only UChicago has a binding ED1 program (they also have EA). You might consider other colleges which have binding programs, as they can really increase your chances, especially since you don’t need financial aid.

You should also consider a college that has an ED2 program, in case your first early application doesn’t work out. NYU, UChicago and lots of other colleges have ED2 programs. These are designed to boost yield, but will work in your favor since you are full pay.

Harvey Mudd’s admission rate is <14%. That would be a reach, not a match.

Thank you for the replies!