Adding an one-out-of-two not null constraint in postgresql

You can use a check constraint e.g.

constraint chk_education check (schoolName is not null or studiedAt is not null)

From the manual:

A check constraint is the most generic constraint type. It allows you to specify that the value in a certain column must satisfy a Boolean (truth-value) expression.

Edit: Alternative to comply with Pithyless’ interpretation:

constraint chk_education check ((schoolName is not null and studiedAt is null) or (schoolName is null and studiedAt is not null))