Detecting the original bandwidth of upsampled recordings
A recording originally at 8kHz and digitally upsampled to 16kHz will have almost no energy in the 4-8kHz range (whatever is here is due to imperfections in the filters used for the upsampling process). I would just use a 4kHz and 5.5kHz high pass; and use a threshold on the signal energy at the output of these filters.

... Unless your recordings are affected by noise, distortion etc. after they have been upsampled to 16kHz. Is that the case? If so, please update your question and tell the whole story about your signals!