the database [is] based on triggers and there is no actual ER-Model which I could use....
There are pretty much no foreign keys.
I must say it sounds like your are being badly advised. You have an academic project, the design of which does not use conventional foreign keys, and that cannot be modeled with an entity relationship diagram?
only using trigger to interact with the tables
Triggers were invented before DRI was defined in the SQL standard. IIRC, they were invented by Sybase, around 1986. If their use is restricted to enforcing referential integrity constraints -- as should be -- they will be used sparingly. Most RI enforcement since the advent of SQL-92 is readily and preferably supplied declaratively in the database schema. Triggers today are properly seen as obsolete and exotic: largely superseded by DRI, and occasionally useful as a workaround in weird situations.
Can database interaction be only through triggers? Trivially, no. A trigger cannot insert new data. Without ridiculous gyrations, a trigger cannot select data to be returned to the application. But in any case that's barely a database design issue: the observations hold, no matter the tables in question.