We have investigated two-dimensional nanostructures of the topological insulators Bi2Se3 and Bi2Te3 by means of temperature and magnetic field dependent Raman spectroscopy. The surface contribution of our samples was increased by using thin films of dropcasted nanoflakes with the aim of enhancing their topological properties. Raman spectroscopy provides a contact-free method to investigate the behavior of topological properties with temperature and magnetic fields at lower dimensions. The temperature dependent Raman study reveals anharmonic phonon behavior for Bi2Te3 indicative of a two-phonon relaxation mechanism in this material. Contrary to this, Bi2Se3 shows clear deviations from a two-phonon anharmonic decay model at temperatures below 120 K exhibiting a hardening and broadening, especially of the A1g2 mode. Similarly, the magnetic field dependent self-energy effects are only observed for the A1g2 mode of Bi2Se3, showing a broadening and hardening with increasing field. We interpret our results in terms of corrections to the phonon self-energy for Bi2Se3 at temperatures below 120 K and magnetic fields above 4 T due to electron-hole pair excitations associated with the conducting surface states. The phonon renormalization with increasing magnetic field is explained by a gap opening in the Dirac cone that enables phonon coupling to the changing electric susceptibility.