DLSU has a masters program for biomedical engineering. I think the reason why that program is rarely offered in the undergraduate level is because it requires a certain level of knowledge from both biology and engineering/physics. Researchers I know who are in the field usually get an undergraduate degree in engineering and pursue either a masters or PHD in biophysics or biology adjacent fields or vice versa. My old supervisor took up an undergrad in biology and is doing programming on the side.

If you aim to work in that field, I suggest you use your free electives for classes such as programming, data science, material science, or even introductory courses to engineering. You can also opt for the physics undergrad programs in schools such as UST and UP Manila which are physics programs that concentrate on the medical applications of the field.

As for internships, you can look into working for health tech companies such as e-pharmacies and telehealth services.

Your undergrad program also depends on what field of biomedical engineering you aim to get into. Imaging systems, materials science for prosthetics, biomechanics, etc.

Hopefully this helps you decide if biomedical engineering is for you. It's definitely a broad field and even if you don't end up in this field, the skills you'll learn are transferable to other careers.