It's very hard getting left-handed strings these days. Even rarer than flat-wound bass strings. Most shops just pass off right-handed strings as left-handed, but if you check closely you can see the bottom three are wound the wrong way, and the top three have the ferrules on the wrong end.
That's not so bad for the top three on a Floyd-Rose trem, 'cause you chop the ferrules off anyway, but for the bottom three I often find I'm confusing my upstroke with my down stroke. I have discovered though that using a right-handed plectrum turned back to front compensates for this nicely.
Of course when picking, the plectrum trick's no good.
Really fast picking makes my nose bleed.