Shear thickening in colloidal dispersions has been well studied in systems with hard sphere and repulsive interactions. Here, formation of flow occluding hydro-clusters has been observed in experiments and simulations and properly implicated in the shear thickening of these materials. By contrast, sticky materials, colloidal systems with attractive interactions, are largely unexplored in this regard and gel forming systems are not known nor predicted to exhibit shear thickening. Dilute dispersions of fumed carbon particles in a hydrocarbon solvent form colloidal gels with typical fractal scaling of elasticity with particle volume fraction. Surprisingly, this attractive, thixotropic system displays shear thickening at high Peclet numbers, where there is a break-down of previously densified particle clusters and concomitant increase in effective volume fraction due to the ramified structure of the colloidal particles. This is in contrast to hard-sphere systems where shear thickening is due to growth of hydro-clusters with divergent contact times. On cessation of high shear flow, these dispersions form shear thickened gels exhibiting a power-law dependence of elasticity on pre-shear stress. We propose a simple model that accounts for the observed behavior, allowing our data to be rescaled onto a single curve for different particle volume fractions. We observe long lived internal stresses that result from a rate quenches into the gel state and find that the shear modulus is directly proportional to the internal stress in the system at a fixed sample age. At short times, t<1000s, the internal stress decays with a weak power law dependence on time. Optical studies reveal that the deformation response of these shear thickened gels is highlighted by the transient formation of highly anisotropic vorticity aligned flocs that appear to be linked to the relaxation of internal stresses in the system.