When one-bond Frenkel dumbbells are allowed to dimerize, as analyzed using the Wertheim theory of association, the resulting fluid exhibits shear thinning or shear thickening behaviors. In contrast, when Gaussian chains undergo shear-assisted association, only shear thickening is possible. The present theory of shear-induced association of non-Newtonian fluids is applied to interpret the shear thickening seen in equimolar solutions of the CTAB (cetyl trimethyl ammonium bromide) micelles and sodium salicylate. Also derived in this study are the frequency dependent Newtonian viscosity and the non-Newtonian viscosity for a dilute Brownian suspension of two-bond freely jointed Frenkel dumbbells.