Chemical engineering has better employment prospects with bachelors than does BME. ChemE covers most of the required pre-med classes, except for bio.
There’s a glut of bio and chem grads so employment with either of those majors can be dicey. There are jobs for those majors but it’s up to you to make yourself an attractive applicant by developing a suite of lab & programming skills needed by research labs and/or industry. There are very few jobs for physics bachelors unless you have programming and data analytic skills and are willing to change fields. (The physics majors I know are now mostly employed as analysts in the financial and airline industries.)
Mathematics, statistics, actuarial science and comp sci all have good employment prospects, but have less overlap with pre-med requirements. Also information science and software engineering have good potential employment post-graduation, but again, much less overlap with pre-med requirements.
If you want something more hands-on–clinical laboratory science (aka medical technologist) has very good employment potential.
Is this going to be an issue w/r/t med school? It’s going to be at least 7-11 years (4 year med school + 3-7 years residency training) after college graduation before you’ll be earning a salary big enough to contribute to your family’s support. And then you’ll likely have substantial debt of your own that needs to be paid off ASAP. (Average med student debt upon graduation is ~$200K plus whatever you owe from undergrad.)
In one sense, medical students need to be selfish. They cannot support their family AND go to med school at the same time.