You're right, but the effect you're interested in is not manifest as a change in the Coulomb potential. Basically you define an interaction potential which is a function of time and space during the reaction and that changes accordingly.
The Coulomb potential is a purely radial potential defined over all distances from the centre of the atomic system, including within the Bohr radius. If two atoms collide with each other with enough kinetic energy such that they are within a Bohr radius of each other and their electron clouds overlap, the interaction becomes extremely messy and is further complicated by the fact that classical physics is no longer appropriate to describe the system. I believe there are numerical simulations of atomic collisions that take into account this sort of thing, but it's mainly a statistical/energy-related problem. Collisions between atoms are currently treated in a kind of "add two ingredients to a box, shake them up and open the box to see the final result".
You might need to be careful not to confuse this with "electron screening", which is the change in the interaction between particles caused by an overarching electron cloud in a plasma. This screening is manifest usually as a change to the equation of state of plasmas or by using "screening factors" to nuclear reaction rates. It is a macroscopic phenomenon.