Mick,
As a Music Educator, choir/band/orchestra director, voice teacher, singer etc. of well over 30 years, Quite often, the best keys for singing are flat keys! I can assure you that you are completely normal, and a good instrumentalist should be able to play in a variety of keys.      
"Traditional" Musicians can sometimes complain about this as, and this is a common cause for difficulty between Musicians. When one plays in the key of F major or d minor, one uses Bb, and certainly if one can play in keys with all of those sharps, then one must be good enough to ascertain where the flats are. There are certainly plenty of tunes with accidentals.
Much of the time, we accommodate "them" by playing in the Trad/Bluegrass/whathaveyou keys. It is only fair that they stretch their Musicianship a little to accommodate you.

I have been playing Guitar since I was a teenager, I am still only 5 ft tall, with quite short arms & fingers. Much shorter than any Traditional Guitarist or Guitar student who has complained to me about Bar chords, I daresay. I can't even wrap my thumb around the neck for the 5th & 6th strings as many pickers do. Yet, I play bar chords! I play Bar chords in whatever key is called for! I even play Beatles songs in the John & Paul Keys! I also have a fiddle which I don't play that well. I can saw out a few tunes. Sometimes I saw along with a Bagpipe CD-in the keys of Bb, Eb, et al.
I know it is not always easy to embrace a new concept when it involves a little practicing, but I say to all those who stand in that rut to dare to break your mind out of the "Bluegrass Keys only" mentality & stop being intimidated by Flats! Don't be a weenie armed Musician. They're all right there next to the naturals. Some Flats in Bb & Eb are even the same exact notes as some of the Sharps you already play. Dare to be different! Become a better Musician, and don't let any key cause a panic attack again.
   What, I ask, is more traditional than a Piper playing in Bb?