While it is harder in some respects for nurses and others who have a specialized health major, you do not, repeat, do not need a second degree, nor do the vast majority of nontrads trying to get into medical school. Depending on your previous academic record, you need to take the proper level of prereqs (that would count toward Bio or Chem majors is rule of thumb) and perhaps some additional advanced course work. If you have a year of General Bio. General Chem, General Physics, Organic/Biochem, all with lab about 35 credits along with strong previous academic work, you may have enough.
The reasons that nurses and other health professionals have the lowest acceptance rate to medical school across a broad swath of majors (see
https://www.aamc.org/media/6061/download ) includes the following
1) showing commitment and motivation: you made a decision/judgement to get a BSN and now you are changing fields. This is particularly to those trying to go directly from BSN UG to medical school. You should have at least a few years working in the nursing field (which I believe you have or will have)
2) Time to prep: If you are working full time in nursing, it may be difficult to find sufficient time to take course work, prep for MCAT and work on the applications.
3) academic rigor: in many BSN programs the course work is specifically designed for nursing and therefore limits the scope and depth of the course. Indeed, most health science course will not be classified as BCPM ("science") for purposes of AMCAS GPA.
4) MCAT scores. Specialized health major applicants have the lowest MCAT scores partly due to the less rigorous coursework and the lack of time to prep for the exam