Yes, this is mould. its from the high humidity in the shower area.
If you have a window, I would leave it open after showers, or better yet, install an extractor fan.
You can remove the mould by getting some 20% Hydrogen Peroxide and diluting it into a spray bottle... just spray on mould and it should go away.
I would add about 10% hydrogen peroxide to your spray bottle. you should see bubbles forming on the mould. The nice thing about H2O2 is that it basically reacts into water and Oxygen, it kills the mould by excess oxygen. so you dont have to worry about unsafe chemicals in your shower.. the only risk is if you used too strong of a mix (more than 30%) H202 of the solution.