It's most likely an ear trumpet. But unfortunately the only images of them appear to show a very distinct shape to these devices, a shape that would have showed in the video.
http://www.hearingaidmuseum.com/gallery/Non-Electric/EarTrumpets/Short Trumpets/index-short.htm
They seem to generally work like this
In the link above, the shapes become more and more distinctive with one end being thin enough to go into your ear. The Otophone, however, seem to be around the same size if you wanted to use it in a way which would make it look like you're holding a mobile phone. I don't know anything about this but those seemed to have been 120 years before this video was made. Maybe she was using one of them, as that seems more likely judging purely from the video. If it's an ear trumpet, then can anyone find one small enough to be held in the way she did in that footage? I've seen ear trumpets being held before in old footages and they were blatantly obvious as to what they were. This, not so much.
Interesting video. I'll try to get an expert to watch it. I'm not sure about the TT theory, but I'm not sold on it being an ear trumpet.
EDIT: Came across some other designs of these.
Most likely using a design similar to the one on the left here. Video is still strange. Her general mannerisms show that she is conversing, or speaking to someone, but none of those around her seem to be walking with her. That's equally as suggestive as what shes holding beside her ear