First, congrats on your obtaining your BArch and a desire to pursue additional education.
As you BArch is a first professional degree, you do not need to pursue the MArch, instead seek a post-professional degree. At some institutions, it may be called a Master of Architecture; at other institutions, it may be called either a Master of Science in Architecture or by another name.
NCARB maintains a list of post-professional degrees available as you may gain IDP credit by pursuing a post-professional degree.
While most accredited architecture programs will probably prefer candidates with a post-professional degree, you may be able to teach with only your BArch if you apply to some programs or seek a teaching position within a community college.
I would advise that you not pursue a post-professional degree ONLY to have the credentials for pursuing teaching; instead, determine what aspect of architecture you wish to pursue and seek a program that fits your interest.