The social and commercial value of digital data in the Internet of Medical Things (IoMT) is currently receiving unprecedented attention, and the security of the data is increasingly being challenged. In recent years, reversible data hiding (RDH) based on interpolation technology (IT) has emerged as an area of activity due to its high bit per pixel (BPP) and peak signal-to-noise ratio (PSNR). However, the PSNR of conventional embedding strategies may not be optimal for a given BPP because they sequentially embed data concerning the difference between interpolated and selected pixels, without considering that embedding fewer bits of data could produce higher PSNR. As such, we propose an adaptive strategy for IT-based RDH that provides the ability to embed into interpolated pixels with fewer bits of data preferentially. First, an adaptive bit allocation strategy (ABAS) with lower computational complexity is developed for a given BPP. Second, we propose an adaptive RDH method using the proposed ABAS and data recoding. The results on BossBase and BOWS-2 data sets showed that the proposed method surpassed several IT-based RDH methods, with average PSNR increasing by ~6.4 dB. Our method also achieved superior performance compared with non-IT-based RDH methods with an average PSNR increase of ~2.6 dB. Moreover, the proposed ABAS was applied to four typical IT-based RDH methods. The results showed that the improved methods increased the average PSNR by ~7.4 dB compared to the original methods. Our method is an expected solution to the security issues of sensitive data transmission in IoMT.