Access to “My Site” is missing from the admin bar

Finally, I managed to solve the problem. And I have to recognize I was somehow arrogant by easily dismissing @MikeNGarret response.

However, he was completely right and I truly apologize.

One of the plugins I was using was causing the problem, so I want to tell those who might have the same problem that the plugin itself is called “Cherry White Label”.

By deactivating it I was able to recover the direct access to my site´s frontend from the admin panel.

As I said when commenting to @MikeNGarret, I was really afraid of losing valuable info just by deactivating all of my plugins. However, I did it one by one and I finally figured out which one was causing all this mess.

Once again, thanks to @MikeNGarret for pointing me in the right direction.