Is there a way I can tell exactly how many polygons are in my model?
In Edit Mode, there are a couple of stats counters in the top-right of the window, Fa: displaying your face count. Now this isn’t terribly useful, since it counts faces, not triangles and triangles is what you want to know. To use an analogy, a face counter is about as useful as a single coin counter is to see how much money you have. It doesn’t work because not all coins have the same value. So just press A to select all and then Ctrl+T to triangulate. Now the amount of faces is the same as the amount of triangles, so the Fa: value is reliable. Then Ctrl+Z to get rid of the triangulation.
If you think this is an absolute crap way of checking something as simple as your polygon count, welcome to the club. It gets even better when you have to join multiple meshes and add Mirror modifiers, look at the triangle count, and undo that all again.