Yes, since the particles are point-like we should expect the force between them to grow without bound if they are very near. I find the calculation for small d

Yes, since the particles are point-like we should expect the force between them to grow without bound if they are very near. I find the calculation for small distances to be unpredictable, one easy way to test it is to place two particles with small gravity and a large attractive charge. Occasionally close passes cause explosive motion, while other times it hardly overcomes gravity.