Remission rates are higher with antidepressants that have dual serotonin and norepinephrine actions as compared to SSRIs (only serotonin), so I can see her rationale for using an SNRI. Tests such as the HAM-D are sometimes administered to measure subjective severity of depression, however a good physician should base her diagnosis off of behavioral observation and a psychiatric interview, rather than the results of a test.
A diagnosis of non-melancholic depression doesn't really tell us much. I suppose it means you aren't having a difficult time sleeping, trouble eating, complete anhedonia or the typical diurnal mood fluctuation (worse in morning, better at night) seen in melancholia. Atypical depression is characterised by reversal of melancholic symptoms. If you are sleeping excessively, craving sweets or gaining weight, and have some mood reactivity (feel better in response to positive stimuli) then you likely have atypical depression.
SNRIs are indicated for both melancholic and atypical depression, however should be taken only in conjunction with a mood stabilizer if a bipolar spectrum disorder is suspected, as an SNRI alone can precipitate a manic or mixed episode and cause rapid cycling.
I am unsure why bipolar II was ruled out, but I am guessing you didn't meet all the criteria for a hypomanic episode. Regardless, cyclothymia or a bipolar spectrum disorder may be present even without a full hypomanic episode and this would suggest that you would do well on a mood stabilizer along with an antidepressant. A psychiatrist would know all this, but your GP may not. I would recommend that you get a referral to a psychiatrist, who will be able to give a more precise diagnosis and thus devise a more helpful medication plan.