She attended language school for one year and polytechnic for one year.
->She attended language school and polytechnic for one year respectively.
Is it right to use 'respectively' this way?
No, I don't think so. At least, it sounds odd to me.
Try these:
She attended a language school and a polytechnic for one year, each.
She attended a language school and a polytechnic for one and two years respectively.
Thanks for your reply, Ruslana.