Can not install a database, can I still learn though?
The easiest way to learn about SQL-Server is to install a SQL Server express.

Even without having an actual website attached to it, Microsoft has a few samples.
And if you want live environment to try out, and see what you can put together, Azure has a free trial.
Which you can use to set up a few vm's.

It's very hard to learn anything from a limited environment, every problem or fault might or might not be caused by something you have control over.
If you want to get the most out of it, set up your own environment.
Or contact whoever is in charge of your environment to see what can be arranged.