Context. Several dusty infrared sources traced on their orbits around Sgr A* with SINFONI and NACO mounted at the VLT/Chile show near-infrared (NIR) excess and Doppler-shifted line emission. We investigate these sources in order to clarify their nature and compare their relationship to other observed NIR objects close to Sgr A*. Aims. Using SINFONI, we are able to determine the spectroscopic properties of the dusty infrared sources. Furthermore, we can extract spatial and velocity information of these objects. We are able to identify X7, X7.1, X8, G1, DSO/G2, D2, D23, D3, D3.1, D5, and D9 in the Doppler-shifted line maps of the SINFONI H + K data. From our K- and L′-band NACO data, we derive the related magnitudes of the brightest sources located west of Sgr A*. Methods. For determining the line of sight velocity information and to investigate single emission lines, we used the near-infrared integral field spectrograph SINFONI datasets between 2005 and 2015. For the kinematic analysis, we used NACO datasets from the years between 2002 and 2018. This study was done in the H, Ks, and L′ band. From the 3D SINFONI data-cubes, we extracted line maps in order to derive positional information for the sources. In the NACO images, we identified the dusty counterpart of the objects. When possible, we determined the Keplerian orbits and applied a photometric analysis. Results. The spectrum of the investigated objects show a Doppler-shifted Brγ and HeI line emission. For some objects west of Sgr A*, we additionally find [FeIII] line emission that can be clearly distinguished from the background. A one-component blackbody model fits the extracted near-infrared flux for the majority of the investigated objects, with the characteristic dust temperature of 500 K. The photometric derived H- and KS-band magnitudes are between magH > 22.5 and magk = 18.1+0.3−0.8 for the dusty sources. For the H-band magnitudes we can provide an upper limit. For the bright dusty sources D2, D23, and D3, the Keplerian orbits are elliptical with a semi-major axis of aD2 = (749 ± 13) mas, aD23 = (879 ± 13), and aD3 = (880 ± 13) mas. For the DSO/G2, a single-temperature and a two-component blackbody model is fitted to the H-, K-, L′-, and M-band data, while the two-component model that consists of a star and an envelope fits its SED better than an originally proposed single-temperature dusty cloud. Conclusions. The spectroscopic analysis indicates that the investigated objects could be dust-embedded pre-main-sequence stars. The Doppler-shifted [FeIII] line can be spectroscopically identified in several sources that are located between 17:45:40.05 and 17:45:42.00 in Dec However, the sources with a DEC less than 17:45:40.05 show no [FeIII] emission. Therefore, these two groups show different spectroscopic features that could be explained by the interaction with a non-spherical outflow that originates at the position of Sgr A*. Following this, the hot bubble around Sgr A* consists out of isolated sources with [FeIII] line emission that can partially account for the previously detected [FeIII] distribution on larger scales.