  We investigate the existence of self-dual solitons with internal structure in
a gauged $O(3)$ nonlinear sigma model immersed in a dielectric medium generated
by a real scalar field (dubbed the source field). We consider rotationally
symmetric configurations and applying the {Bogomol'nyi-Prasad-Sommerfield}
formalism to obtain the energy lower bound and the respective {first-order
differential equations (or self-dual equations).} By solving such a system of
equations for three different dielectric media, we find the internal structure
generates relevant changes in the soliton profiles when compared with the ones
obtained without the presence of the dielectric medium.
