It is certainly possible to have finished in 3 weeks (what, by you, is "finished"? What was your OG? Your FG?). Hydrometers don't generally lie... although Walker would say that they might bend the truth a bit.
For carbonating, I would use... I think... a half-cup of honey? I'm trying to remember. Dissolve it in hot water, stir it in.
And definitely give your mead some time in secondary. You can almost throw it into storage and forget it a while.
Lion's Den Brewing
Primary/Lagering: April-zen Festbier
Drinking: Starburn Spiced Amber
Drinking: Regulus Rye/Wheat with a bite
Drinking: George Takei's O My-bock