Other study options
While waiting for your case to be evaluated, it's possible for you to begin studying Swedish. There are organisations that provide these and other types of courses for asylum-seekers.
Sweden has a long history of providing courses at various levels for interested students. There are folk high schools, adult education schools and vocational studies, to name a few. Municipalities offer a course called Swedish for Immigrants (SFI) for newly arrived individuals. In most cases, however, you must have a residence permit in order to begin your studies.
It can be good to read up on the various options available to you so that you're prepared when you've received your residence permit. You can find more information right here at Studera.nu.
Options for learning Swedish
There are various organisations that provide support to asylum-seekers. Some offer classes that can help you learn Swedish. Informationsverige.se, a website for asylum-seekers in Sweden, has a great information page about learning Swedish.