A Fistful of Sky — Nina Kiriki Hoffman

Gypsum LaZelle had nearly given up. She'd already watched her two older siblings experience the transition -- the sudden, debilitating process that turned them from ordinary children into mages, gifted spellcasters like their beautiful mother. Perhaps she was a late bloomer, she thought until her younger siblings came into their powers as well. Now, at twenty, Gypsum fears that she must accept her fate: a mundane life without magic.
 
She can live with being ordinary, an outsider. After all, someone in the family had to take after her father…But one day, alone at home wither family away, Gypsum falls terribly ill. And when the symptoms pass, something has changed. Something she's dreamed of for such a long time -- and suddenly, isn't ready for at all.
 
“One of the most original and important writers of fantasy working in America today.” -- The New York Review of Science Fiction