What grade are you in currently?
BSMD has its own unique requirements that include things beyond academics: physician shadowing, community service w/ disadvantaged groups, clinical experiences. If you haven’t started participating in these activities and you’re a junior, it’s way too late to start now and still be considered a viable candidate for BSMD programs.
Premed honors is a kind of oxymoron. All pre meds are expected to take hard classes and do very well in them. Whether or not they take those hard classes thru the honors program at their home university is irrelevant. Participating in the honor program at a university has zero influence on a pre-med’s ability to get accepted to med school.
Typically honors programs do not offer special opportunities for pre meds to get clinical experiences nor do they find research labs for them to volunteer in. Pre meds are on their own for that.