The idea of exchange particles is a purely quantum mechanical concept and does not extend to macroscopic bodies where we have the concept of classical fields.

Your assumption about an infinite amount of particles being exchanged giving an infinite force is incorrect. Perhaps you mean infinite corrections in QFT? The answer to this is in a process called renormalisation. Nevertheless, the numbers of particles is not infinite and so there is no need to think about infinite forces.

You can read about renormalisation on Wikipedia.

The idea of exchange particles is a purely quantum mechanical concept and does not extend to macroscopic bodies where we have the concept of classical fields.

Your assumption about an infinite amount of particles being exchanged giving an infinite force is incorrect. Perhaps you mean infinite sums in QFT? The answer to this is in a process called renormalisation. Nevertheless, the numbers of particles is not infinite and so there is no need to think about infinite forces.

You can read about renormalisation on Wikipedia.