  In the present work we are concerned with the following
Kirchhoff-Choquard-type equation $$-M(||\nabla u||_{2}^{2})\Delta u +Q(x)u +
\mu(V(|\cdot|)\ast u^2)u = f(u) \mbox{ in } \mathbb{R}^2 , $$ for $M:
\mathbb{R} \rightarrow \mathbb{R}$ given by $M(t)=a+bt$, $ \mu >0 $, $ V $ a
sign-changing and possible unbounded potential, $ Q $ a continuous external
potential and a nonlinearity $f$ with exponential critical growth. We prove
existence and multiplicity of solutions in the nondegenerate case and guarantee
the existence of solutions in the degenerate case.
