Tuning up from concert and any guitar puts more strain on the neck. Period. Nylons (full size) have already got 120 pounds pressure. That's what it is 'stressed' for or 'built' for. So, your choices are

1) get a better capo (as was suggested)
2) learn other keys
3) go to an open tuning (which will still at times require a capo if you don't do Barre chords)

That's all I can suggest. Good luck.