The propagation of a relativistic electron bunch through a plasma is an important problem in both plasma-wakefield acceleration and laser-wakefield acceleration. In those situations, the charge of the accelerated bunch is usually large enough to drive a relativistic wakefield, which then affects the transverse dynamics of the bunch itself. Yet to date, there is no fully relativistic, fully electromagnetic model that describes the generation of this wakefield and its feedback on the bunch. In this article, we derive a model which takes into account all the relevant relativistic and electromagnetic effects involved in the problem. A very good agreement is found between the model and the results of particle-in-cell simulations. The implications of high-charge effects for the transport of the bunch are discussed in detail.