If the "AM" is DSB-SC AM you would simply multiply by the carrier frequency and low pass filter in order to demodulate. We can determine more by observing your filtered signal with time (as a waveform) - including how to extract the carrier, can you plot that as well?
Short of that, assuming it is a DSB-SC AM modulation, I suggest the following as a simple demodulation technique (that I just made up so requires critique if this would actually work):
Multiply the filtered signal of the modulated signal alone by alternating an alternating sequence of +1 -1 at the sampling rate. This will invert the spectrum such as to move the modulated and spectrally symmetric waveform to a lower frequency (call it carrier-x, which given carrier at $f_1$ with Nyquist frequency $f_s/2$, carrier-x will be at $f_s/2-f_1$) where we can simply square the waveform (if DSB-SC) to determine the carrier frequency (meaning multiply the waveform with itself, as in $x^2$). This will produce a strong frequency at twice the carrier frequency with the modulation stripped. For post processed demodulation, play this extracted carrier at half the rate by inserting zeros between each sample (this will stretch out the recovered carrier to half rate, and produce additional carriers at harmonics, but I believe the subsequent filtering should reject those components so as to not require additional interpolation filtering), and then multiply this directly with the modulated signal at carrier-x. Low pass filter this result (given the plot the OP provided, a low pass filter at 1 KHz appears sufficient, but it should be less than $f_s/2-f_1$, and the intention is to block the doubled result that would appear at $2(f_s/2-f_1)$.
Unless it is known that this message is hidden audio, I would suspect that it is a data pattern, such as a signature tag.