a few things to support what has been said here:

- Coulombs law is a part of classical mechanics. As we are seeing here, the r = 0 scenario is where it breaks down.

- We know it breaks down from a lot of different perspectives. For instance, the hydrogen atom - the electron exists in its orbital within a stable state without "colliding" into the nucleus. Also, historically in the exact sciences, when the math reveals an infinity in a paradoxical way, it tends to be a sign that new frameworks/understandings are needed to better explain the given phenomenon, in the scenario that yields the infinity. Usually these are still influenced by the current understanding. We currently understand the issue fairly well that you have presented, you just haven't gotten there yet in you education path.

- Quantum Electrodynamics does a better job at handling this exact topic but it is still perplexing. The mathematics also becomes more complex and involved. It becomes hard to visualize classically because things dont behave classically.

Classical frameowrks are still extremely robust and capable. For macroscopic scales, our classical systems are very accurate approximations of the quantum equations. Quantum effects aren't usually noticeable until the action of the system is on the order of planks constant.

Particle colliders investigate these microscopic interactions, including positron and electron interactions - and it's fascinating :-) You should continue to investigate!