Here's from someone who is switching from ENGR to Accounting.
MBA is for more general courses (IB, PE). Only do MS acct if you only want to work in accounting for the foreseeable future.
Most MS schools require you to either take some foundation courses in Accounting (Intro, Intermediate, Audit, Tax) and some will require additional courses (Finance, Mkt, Org Behavior.) It is rather late in the cycle to apply now, but IF you want to start this fall then you need to apply now and also maybe take some summer courses (preferably at a 4 year college, can be distance based). Some schools offers boot camps or requires you to be non-acct majors to qualify (See USC and UNC and Villanova)
Otherwise instead of the standard curriculum you may need to take additional courses there to graduate (additional summer or so.)
Take the GMAT, and learn about acct ASAP
Good luck applying!!!