what kind of career that doesn't involve blood in medical school?

There are types of physicians (radiologist, psychology) who do not really have to deal with blood when they are working. But, as you probably know, all physicians have to do to medical school, and in medical school you will have to deal with blood.

In medical school, you will have to take anatomy, and there, you will have to participate in dissecting the cadaver (the dead body you saw at Harvard). You will have to do a surgery rotation, where people are being operated on--there will be blood. Then in residency, no matter what specialty you choose, you will also have some exposure to blood. Even if you are doing Radiology and Psychology, you have to spend some time in Internal Medicine.

If you really want to be a doctor, you'll have to get over being sick of blood (or bad smells or other things related to the body). For some people, after they spend a few months are the things that they think are "gross", they usually get over it, or decide that being a doctor is not for them. It's good you're asking this question now--how badly do you want to be a doctor? Are you will to deal with feeling sick in order to do that?