Upvote:2
The status of refugees in Germany can differ:
Those whose status is not yet settled may come under the Dublin III regulation. While in Germany, their travel may even be limited to a single administrative district.
Generally speaking they will always have a right to leave the EU, but no right to travel within the EU or even within a member state.
Upvote:3
YES you can try to visit again. That does not mean anything will change, you can still be denied entry if your circumstances have not changed and it is determined you still do not qualify for entry.
Make sure you don't have a ban. Review the document you were given when denied entry.