I kept my own long manicured nails with a/c, (adriamycin/cytoxin) and it felt good to hang on to these after my hair fell out!!!
I had your experience with Taxol though, my eye lashes/brows went along with broken nails
Its best to keep them short for a time and hopefully no more will break off!! Mine were so long when they broke off I had to plaster's over them
It will pass once the tx is over so hang in there