Im on Effexxor myself and always feel tired. I also suffer from heavy anxiety but looking back didnt notice it causing tiredness. Although I suppose being stressed from the anxiety could be causing sleep problems. Tell your doctor about your sleep troubles and take some light medication to help with it. There are a bunch of non-addicting medications you can try like Gabitril or Mirtazapine, both arent used commonly for sleep aid but work pretty well and dont knock you out but rather give you a higher quality of sleep.

Feeling sleepy all the time really sucks though! Good Luck with it.

-Mark