We demonstrate comprehensive investigation of the injection locking dynamics of a backscattered Brillouin laser in silica whispering-gallery-mode microcavity. Via injection locking, the Brillouin laser acquires highly correlated phase with the seed laser, enabling ultra-narrow bandwidth, high gain, and coherent optical amplification. Also, for the first time, to the best of our knowledge, the injection locked Brillouin laser is utilized to implement all-optical carrier recovery from coherent optical data signals. We show that by using the injection locked Brillouin laser as a local oscillator for self-homodyne detection, high-quality data receiving can be realized, even without traditional electrical compensations for carrier frequency and phase drifts.