I've been playing for years and my fretting hand still sometimes aches when I play barre chords for an extended period. One thing you should watch for is applying more force to the strings than is really necessary; I tend to do that, and it makes stress on the fretting hand worse. As others have already mentioned, F is probably the most difficult to play as a barre chord because of proximity to the nut. Depending on the piece, there are a couple of alternatives you might use to the F barre chord.
What we think of as the open-position F chord is really just a variation on the F barre chord, leaving out the 5th and 6th strings. If the piece can do without those bass notes, the open F chord puts less stress on the fretting hand. Depending on the size of your hand you might also fret the 6th string with your thumb, which would eliminate the need to barre at the first fret.
Mark