Hello Jessica Schneider,
Out of the box, I don't believe it's possible to create callout labels in Portal for ArcGIS Web Maps.
With that being said, it looks like it's possible with some coding knowledge. Here (Using callout lines with labels | ArcGIS API for JavaScript 4.14 ) is the documentation regarding this functionality and here (Using callout lines with labels - 4.14 ) is a live example.
Best of luck,
Joe