Upvote:1
As far as visas are concerned, a type D visa gives you rights similar to a type C short-stay visa to be present in Shengen outside the issuing state for 90 of every 180 days.
However, also like a short-stay visa it does not give you any right to work outside the issuing state. The Belgian authorities may consider your internship to be work (I don't know how they define it, but it is rarely just a question of whether you get paid or not), in which case you could get into trouble quite independently of the visa situation.