Unknown Lamiaceae plant identification
I'm going to take a stab at this. If your plant is not particularly aromatic, I feel pretty confident it is Lycopus uniflorus.  There are good descriptions here and here.  In particular, the description of the flowers at the Minnesota site, as having 2 purple-stemmed exserted stamens seems to match your flowers.  Apparently this species should have a tuber (should you end up digging yours up), while Lycopus virginicus which is probably a good second guess does not have tubers (see the differential description at the bottom of the Minnesota page).

Updated and Revised Answer

With additional pictures of now more mature flowers, which are clearly lilac in color, and the info that the leaves are strongly minty smelling, we'll revise the answer to Mentha arvensis, which fits all the available info. More here.