I would be very surprised if you were having an allergic reaction to the metals in your guitar strings. However if you really want to know, go see a GP.
Id keep using fast fret and just keep on going. I think this is a problem that will either disappear in time or you will just have to live with !
You can also get Teflon (?) coated guitar string, which may help. They sound a little different from regular strings however they may be worth a try.
Check out:
http://www.musiciansfriend.com/srs7/sid=030315085025012217250242461215/search/g=strings?q=coated+string
My instructors page and www.studiotrax.net for all things recording.
my toons Brought to you by Dr BadGAS
my toons Brought to you by Dr BadGAS