Ah, welcome to the analytical, mono-syllabic language that is Vietnamese where words change their meaning very subtly depending on context and position. Very tricky. Còn...nữa = Also. My knee also hurts (or Also, my knee hurts). Vẫn = still. I still live nearby. She is still a journalist. However, this is where you'll get confused. "Vẫn còn" (1 word) = still. Tôi vẫn còn ở gần đây = I still live nearby. Còn by itself (without nữa) can mean both "still" and "also." Tôi (vẫn) còn yêu cô ấy.I still love her. Anh (vẫn) còn ở gần đây không? Do you still live nearby? Bà ấy còn là nhà báo. Here the meaning is not exactly sure. Depending on context, it could mean still or also. For example, Ngoài việc viết văn, bà ấy còn là nhà báo. Beside being a writer, she's also a journalist. Bà ấy còn là nhà báo không? Is she still a journalist? Vẫn còn, bà ấy còn là nhà báo. Yes, she's still a journalist. In summary, còn...nữa = also Vẫn = still Còn = still or also depending on context. If you want to make sure you are understood correctly, use vẫn còn to mean still and use the còn...nữa structure to mean also. Cheers.

Tôi còn bị đau ở đầu gối nữa. The sentence above can be translated as following: Also, my knee hurts. So, the word "còn...nữa" here means "also, addition..." rather than still. As you probably know, you use "còn...nữa" in order to add more information into your speech. And, you are right about "vẫn". It exactly means "still". Hope it would help. Feel free to ask if you are still confused.

In general: còn...nữa = also, too vẫn = still Cheers.