NO. Absolutely NO.
First of all, Case Western is a very good university, and is specifically very good for premed students. You are already in at a university that is an excellent choice for a premed student.
Also, the ranking of the university where you got your bachelor’s degree is not important for admissions to medical schools. You grades will be important, including your grades in tough premed classes. Your MCAT scores will be important. Your experience in medical environments will be important. Your letters of reference will be important. Both getting medical shadowing opportunities and getting good letters of reference will be helped if you know your professors, and staying at one very good and moderate sized university will help you to get to know your professors.
Also, medical school is very expensive. The scholarship that you got from Case is a BIG DEAL. This is going to help you quite a bit when it is time to pay for medical school.
No one in my immediate family is an MD nor DO. However, three people in my immediate family either have graduate degrees that are medicine-related, or are currently studying for a graduate degree that is medicine-related. One got a bachelor’s degree at a university ranked somewhere in the 100 to 140 range and then got two closely related and medicine-related master’s degrees at an Ivy League school. One got a bachelor’s degree at a university ranked in the 100 to 140 range and is about to get her DVM at a university ranked in the top 5 in the world (she will be called “doctor” in about 6 weeks but her patients are large animals). One attended a small university in Canada that you have probably never heard of and is currently getting a PhD in a biomedical field at a very good university that is ranked in the top 20 in some rankings and top 30 in most rankings. All of them report that the other students in the same graduate programs came from a very wide range of undergraduate schools. I know two doctors who got their MDs at highly ranked universities and who told me that the other students in their program came from “all over the place” (this is an exact quote from one of them).
Let’s suppose that you do complete your bachelor’s degree at Case Western, and then let’s suppose you get accepted to a “top 20” university for your MD. In this case, you will probably find that quite a few students in the same MD program, possibly a majority, came from universities ranked about the same or lower compared to Case. They really will come from all over the place. What they will have in common is that they got a high undergraduate GPA in very tough classes, they had very good medical shadowing experience, they got great scores on the MCAT, and they had great references.
Case is also a good size for a premed student. It is large enough to have quite a few excellent professors and a range of majors and classes available, but small enough for you to get to know your professors. It really is an excellent choice.
If you get accepted to any of your waitlist schools, I still would not go there unless you get comparable financial aid that you got at Case, and even them maybe not. Case Western really is that good, and the $35,000/year merit aid really is going to be important over time.
Your premed classes are going to be full of very strong students. I think that you will be surprised (and maybe stunned) how many strong students you are going to meet. You will be competing with these students for grades in tough classes. At least some and possibly all of your premed classes are going to be tough. You are going to have some very tough exams (almost certainly tougher than anything that you have ever seen in your life).
You should show up at Case ready to attend every class, sit near the front if you can, always pay attention, and stay way ahead in all of your studying and homework if you possibly can. If you are ahead in your work, this will help you pick up just a little bit more in every class, and you will want to learn as much as you possibly can and do as well as you possibly can.
You have a great opportunity coming up in September. Congratulations and best wishes!