We propose and numerically investigate a new particle retention mechanism for particle entrapment in creeping flows in a constricted section of a saturated rough-walled narrow flow channel. We hypothesize that particles, whose size is smaller than channel width, can be temporarily or permanently immobilized in a flow channel away from channel walls due to particle-particle and particle-wall repulsive potentials, and, consequently, the flow field is clogged temporarily (coughing) or permanently (choking). Two mathematically simplified repulsive particle-particle and particle-wall interaction potentials are incorporated into a two-dimensional colloidal lattice-Boltzmann model. These potentials are two-body Lennard-Jones 12 and screened electrostatic repulsive potentials. Numerical simulations reveal that unlike in smooth-walled flow channels, particles are entrapped away from rough-walled channel walls and subsequently clog the flow field if fluid-drag and repulsive forces on particles are in balance. Off-balance forces, however, could result in temporary clogging if repulsive forces are stronger on the advancing edge of a particle than on its trailing edge. The new conceptualization and two-particle numerical simulations successfully captured (i) temporary entrapment of two particles (coughing), (ii) temporary entrapment of one of the particles with permanent entrapment of the other particle (coughing-choking), and (iii) permanent entrapment of both particles (choking) as a function of repulsive interaction strength.