We present a multi-wavelength study of the Galactic Luminous Blue Variable HR Carinae, based on new high resolution mid-infrared (IR) and radio images obtained with the Very Large Telescope (VLT) and the Australia Telescope Compact Array (ATCA), which have been complemented by far-infrared Herschel-PACS observations and ATCA archive data. The Herschel images reveal the large-scale distribution of the dusty emitting nebula, which extends mainly to the North-East direction, up to 70 arcsec from the central star, and is oriented along the direction of the space motion of the star. In the mid-infrared images, the brightness distribution is characterized by two arc-shaped structures, tracing an inner envelope surrounding the central star more closely. At radio wavelengths, the ionized gas emission lies on the opposite side of the cold dust with respect to the position of the star, as if the ionized front was confined by the surrounding medium in the North-South direction. The comparison with previous data indicates significant changes in the radio nebula morphology and in the mass-loss rate from the central star, which has increased from 6.1$\times10^{-6}$ M$_{⊙}$yr$^{-1}$ in 1994-1995 to $1.17\times10^{-5}$ M$_{⊙}$yr$^{-1}$ in 2014. We investigate possible scenarios that could have generated the complex circumstellar environment revealed by our multi-wavelength data. ; Comment: MNRAS, in press