URochester is a particularly strong prospect here. Not only is it a very strong school for both BME and life sciences, but it also has an unusually high percentage of international students (about one in four undergrads are international). URoch relies on full-pay international dollars to fund their financial aid for domestic students, so a student like you, with both a strong record and full government funding to attend, will be an attractive candidate there.
Northeastern is another school that favors full-pay international undergrads. It’s reachier than Rochester (mostly because the Boston location is in higher demand) but certainly possible with your stats. The co-op model would allow you to access US work experience. And they have a combined Bioengineering/Biochem major that could be a good starting point - you could stay in the combined major, or shift into either of the single majors if you find you prefer one over the other. Bioengineering and Biochemistry, BSBioE | Northeastern University Academic Catalog Great urban setting; it’s a little larger (16K undergrads), but with a very manageably-sized campus. Also in the Boston area, Tufts could be a great reach school as well, and they also have a combined-degree option https://engineering.tufts.edu/bme/current-students/undergraduate-program
Lots of great smaller options if you don’t need to keep the engineering option open, but tougher to find BME at smaller schools. AustenNut already mentioned some of the best options in that regard. There’s also Trinity College in Hartford, CT, which offers a general engineering major with a BME concentration. This is another urban school, with about 2200 undergrads.
Marquette was mentioned - there’s also Milwaukee School of Engineering in the same city (which has a lot to offer!) with around 2600 undergrads - great for engineering, and they have both BME and chemical/biomolecular engineering, but they do not have non-engineering life science majors.
Good luck! Lots of great possibilities for you, if you can narrow down what you’re looking for.