One year of HS science for ADMISSION, not necessarily as sufficient preparation for Che 1210–which is the gen chem class for bio & chem majors (and all pre-meds regardless of their major).
The [pre-health program](Pre-Health Advisement | St. John's University) at St John’s is merely advising and plus a timeline of suggested activities & classes posted to their website. This is not anything unique or special. Nearly every US college has a health professions advisor and holds regular meetings to inform pre-med, pre-dent, pre-vet, pre-PA, pre-PT, pre-OT, pre-any health profession student of the basics. The health advising office doesn’t find you volunteer slots or physicians to shadow. They don’t give you a list of programs to apply to, or walk you through the application process. They don’t provide MCAT prep. They just dispense advice (which can sometimes be terrible! since not all, perhaps even not most HP advisors have any particular training in health professions admissions policies & procedures.)
“Good” has a pretty hazy definition. How do you define good?
St John’s, like most any other college or university is the US, is a good enough school for a pre-med.
Just about any college/university in the US or Canada will offer the coursework you need to satisfy med school pre-reqs. Except for biochem, they’re all low level/intro level classes. You could even find most of them at a community or junior college. Med school admission officers really don’t have a huge preference about what undergrad an applicant comes from so long as they graduate from an accredited 4 year US or Canadian college or university.
This is a problem entirely inside your own head. You’re going into the college admissions process with entirely the wrong attitude. It’s terribly counter-productive to have a “dream” school. It’s Ok to have a dream (becoming a doctor), but you need to be open the many alternate pathways that will get you to your dream.