No, your record label is not your Publisher, unless the record label 1) establishes itself as the Publisher of your songs in your label contract, 2) registers your songs in royalty collection societies, and 3) collects the Publishing royalties and distributes them to you. If your record label claims to be the Publisher but you have never received any Publishing royalties (performance, mechanical, etc.) from your label or from your chosen PRO, then you should confront your record label about this issue.
The record label is the entity responsible for releasing your master recordings to the public on retailers, streaming services, radio, etc. A huge part of a record label’s work involves promotion and marketing of the music as well. Think of it like this: The record label is to master recordings that the publisher is to musical compositions. However, note that it is not uncommon for some record labels, especially the majors, to launch publishing divisions in order to exercise more control over the music they release by exploiting the compositions for licensing opportunities, assuming ownership of the compositions for registering songs and collecting all publishing-related royalties, etc. (Think Warner Chappel Music; the publishing division of Warner Music Group, or Universal Music Publishing Group; the division of Universal Music Group.)