Any student can borrow the Student Federal loans which are $5500 Freshman year, $6500 Sophomore year and $7500 Junior and Senior year. Personally I have heard and seen of successful Medical school admissions from SDSU, Cal Poly Pomona, Cal Poly SLO and even Humboldt.
Again, it is more about taking advantage of the opportunities you are given vs school prestige.
Regarding your lack of some academic courses: You will be evaluated in the context of what your HS offers so you cannot take classes that are not available. If you are able to possibly enroll in some CC courses for Senior year, then it would definitely help and show initiative.