ok so first off nice profile pic, Where do you work now or what kind of jobs could you get with your degree? It kinda worries me that it might be to specific of a degree (biochem) vs just chem ya know?
This might not be what you want to hear, but the only job that a biochemistry undergraduate degree qualifies you for is basically a laboratory assistant job. Most lab assistant/technician jobs tend to be in biochemistry these days, though no one really cares which area of science you majored in so long as you can demonstrate some laboratory skill. These jobs are actually quite decent, if you are good at the hands on lab stuff, but are quite hard to get, given the pay etc.
Beyond that, and sometimes people choose this path after working at a lab assistant job, is postgraduate studies to become a scientist. Again, biochemistry is a very competitive field so you have to love it and want to work hard to do better than others if you want to remain in that field. You don't necessarily have to do a PhD in the same field, you can take on whatever science field you like, provided you understand any prerequisite knowledge, and can convince a supervisor to let you take on a project. it is hard to say more as I don't know what country you come from and the PhD programs can vary quite a bit (some have entry exams, some require a coursework masters first - in Australia, you typically do an undergraudate honours year, which requires a research project/thesis).
Apart from that, there are just the generic graduate entry programs in a wide variety of fields, also competitive in their own way, but if you can demonstrate that you have other relevant skills on your resume, then a science degree can be a positive versus a less difficult to obtain degree.
I guess this includes graduate entry medicine, dentistry, psychology further education programs too.
I have a BS in Biochemistry. The most abundant jobs in my area for someone with my degree is food testing. With that job you need experience in microbiology. I spent more of my time in school focusing on molecular biology, including a research rotation I did for a graduate program I ultimate quit. And I have only had 1 interview relating to molecular biology. If you don't plan on getting an advanced degree, then be prepared to work a lot of 6 month contract-to-hire positions for less than 15$ an hour.
I actually decided to go back to school and add a Medical Technology major onto my BS so that I can work in a hospital lab and actually make a living wage. There are several people with biochemistry majors doing the same thing as I am. It's extremely competitive. Do a lot of research and internships if you can. Companies want experience.