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A Computer Science major leads to a career in Information Technology with career paths in Computer software or hardware to put it very very simply. There are of course many avenues within this great field but that is a separate discussion since your question is not directed towards that.
In order to become a doctor you will need to pursue a very different major in college. There requirement is to study Biology and related subjects. Usually students wishing to pursue a medical degree will be enrolled in a pre-medical focus program. At the end of graduation you will need to take a competitive examination known as MCAT that along with several other factors determines your eligibility to enter an MD program.
As far as working with patients is a very broad topic that includes behavioral aspects, your own personality and whether you would like to work in a fast paced dynamic hospital environment and have a passion for securing the well being of people.
However as a Computer science major you could also focus on gaining skills that are related the application of information technology to Healthcare which is a fast growing field due to Healthcare lw mandates requiring electronic connectivity of many healthcare systems.
I hope that this provides some basis of understanding your career focus.