It's disappointing to discover the career we thought we wanted doesn't offer the satisfaction we'd hoped. We always advise people to talk with professionals in the position they think they'd like before pursuing any career path. Sometimes the reality of the job isn't what we envision. Doing research up front can head off this kind of mistake. You're lucky. You discovered in three short months what takes some people years to find out.
Since you enjoy working with people and performing a variety of tasks, you might consider working in a personnel or administration function. If you'd prefer more autonomy, you also might consider a career in sales. These types of jobs will allow you to use the skills you most enjoy. Combine this with your knowledge of biochemistry, and you may be able to have the best of both worlds. So as not to discard the knowledge you've acquired, look for ways to stay in biochemistry but in another type of job. Working at a pharmaceutical company is a good option. You also might try medical-research firms, plant and animal breeders and growers, food processors, industrial-production and inspection firms, and environmental-protection organizations.
As for your education, if you haven't finished your program, do so and get your degree. Until you've settled into a new career, it isn't prudent to guess what kind of additional education will benefit you most. If you find further study is necessary down the road, the kind of program you should pursue will become clear.