"I wear a jacket."
A propos. For me kurtka is more like a short coat, or the type of jacket you put on when you go out. What I'd normally call a jacket, a suit jacket, for example, is "marynarka" for men, or "żakiet" for women.
That is "I am wearing a jacket", right now.
Unfortunately "na sobie" wasn't introduced in this course and we still have a mess with the accepted answers in some sentences. But technically "to wear" and "nosić" should be the only accepted verbs.