25 years old couple looking for accommodation for summer semester (April - July) in Berlin

I am a student from Prague and with my boyfriend we are looking for flat or room in Berlin from April to the end of a July. We would like to live in dormitory but the problem is that we are from different Universities (Potsdam Uni, Berlin school of economics and law), so we don't know if it is possible to live together while studying in different Uni. In our country is dormitory provided by Universities separately. Otherwise, we would love to accept any advice about renting an apartment/room in Berlin and beware of any problem. The location of the dormitory/apartment is also important (ideally south/west Berlin), while I must travel every day to Potsdam, and the prize is ideally around 200-300 eur per person.