As a biomedical engineer your "end users" are mostly patients, and health care professionals and your "playground" is the wonderful world (in my opinion) of health sciences. You will typically work in a hospital, research center, health industry, health agencies, NGO.
As a chemical engineer you will be developing products, formulas, process for the industry in general so your end user may vary from food, pharma, gas and oil and many other domains.
The way I see it is that during your biomedical engineer day you will need to fulfill/resolve concrete needs or issues (see the recent COVID-19 impact on the lack of ventilators in hospitals) whereas in your chemical engineer day you might spend most of your time in resolving more conceptual challenges.
I hope this is helpful
Best of luck
Sophie recommends the following next steps:
Biomedical engineer works on medical devices. It's a blanket term that could apply to specializations such as mechanical, electrical, systems engineering etc. Day-to-day activity would depend on your specialty, and I would say its not very different from engineers in other industries. There could be additional focus on reliability and documentation because the device may need to be approved by FDA. It is for people who are excited about making products that impact people's medical outcome.
Chemical engineer works on formulation and manufacturing of products like drugs, food and various plastic products. Day-to-day activities includes modeling the reaction/mixing in a chemical reactor, designing the manufacturing process, and applying your engineering and chemistry knowledge to solve practical problems in making a product.
For example, in both chemical and biomedical engineering you may need to conduct very small scale experiments in controlled environments to prove a theory before bringing your intended product or process to scale. You may spend days or weeks building prototypes or choosing the right chemical mixes, then collecting data from your tests. These require meticulous planning and not getting bored of the mundane.
Once you run your experiment and collect the data, you leave the realm of science and move into the engineering- how to apply what you learned to the task at hand. Both fields require that you interview the end user, whether that is a person receiving a pacemaker implant or an operator of an industrial manufacturing plant. Both require using probability and statistics and math in general to scale up your work. And both require collaborative design, working in a team and making adjustments as you go.
As far as differences, biomedical is more closely associated with mechanical engineering if you are doing product design, like making implants or pacemakers, so think more hands on and interactive and building things. Often, unless you are doing DNA splicing or blood transfusion work, you are trying to make a product that can apply in most human bodies. In chemical engineering, you do a lot of math and understanding chemical properties and how they will interact in specific scenarios, such as at a plant, in a river, in a battery. In this closed system, what happens if I add an amount of X to an amount of Y. I would say you are more likely to spend your day in a lab or office environment as a biomedical engineer, though you may find yourself in a university or a hospital. As a chemical engineer, you may spend your day on site in a facility that makes a product (paper, power, plastic, water treatment, etc.) but could also be in a lab or office.
I think there is some overlap and an education in either will prepare you to solve problems at a micro-scale using niche scientific expertise. To help you decide, I recommend you think about some the applications that get you excited-is it building every-day products that anyone could use in their homes, or building life-saving products for people with rare illnesses? Also think about reaching out to people who do those jobs.
Some companies to look into: Boston Scientific, Kimberly-Clarke, GE Healthcare for Biomedical; Exxon Mobile, Sandia National Labs (and other National Labs), Nestle.
Here's a good article: https://careertrend.com/type-companies-people-chemical-engineering-degree-work-at-33626.html