Check the cavble inside of the shifter to be sure that it has not begun to fray, which is causing it to get hung up. Catching it before it breaks is much to your advantage since getting the broken-off end out is a miserable chore.

With the bike in a stand or upside-down, pull on the exposed cable and see if you can shift that way, while pedaling of course. This will help to sort out whether it is the shifter or elsewhere.