meanwhile you can insert thin paper stripes in the nut slots as an emergency treatment.
You wouldn't believe how many guitars i get from proffessional musicians that have this done. . . i am not saying its not OK as an emergency treatment, whatever gets you through a gig. If its on there for more than a week you are being lazy. People spend so much money chasing perfect tone i cant believe they think a piece of paper in the nut is ok .
rant over. . .
mavet's advice is good, fret at the third fret and see how much it clears the first fret by.
You should be able to get a peice of paper between the fret and the string. If the string is pressing on the fret then the nut is too low. the proper fix for a floyd rose nut would be to remove the locking nut and put a thin shim underneath, a small rectangle cut from a drinks can works quite well - dont use paper!!!
If the shim you use is too thick you will obviously need to lower the strings in the nut again to compensate - this is where nut work gets tricky because its very easy to cut them too low and have the problem you started with.
Its also worth checking various parts on the guitar for sympatehrtic vibration that can cause rattling. maybe the string clamps or tuners or buzzing in the open positions. I use a small amount of blue tack attached to parts to see if it stops buzzing. When i find the source i sort out a longer term solution