> I think the shell theorem says that the gravitational forces cancel if you are on the inside of a hollow sphere and all mass is on the surface.
No, it's stronger than that. It says that any spherically symmetric distribution of matter outside a certain radius exerts no "gravitational force" on anything inside that radius, whether there is matter inside that radius or not.
What if my distance to one point on the shell was zero? Would I not feel infinite acceleration towards the massive point on the shell that I was infinitely close to?
> What if my distance to one point on the shell was zero?
Then you are not inside the shell, you are on it. The shell theorem only applies if you are inside the shell.
> Would I not feel infinite acceleration towards the massive point on the shell that I was infinitely close to?
In General Relativity, matter is not viewed as point particles. It is viewed as a continuum, described by the stress-energy tensor. This is one of those cases where the difference shows up.
I think how gravity works at really short distances like 10^(-50)m is still a mystery as we don't have a consistent quantum theory of gravity that works there.
But as you get close to stuff, say two atoms, the electrostatic and other forces are far greater than the gravitational ones.
Any point on the shell, whether the shell has zero thickness or not, has zero mass, but a finite mass density is assigned to it. Any finite mass is spread out, so you cannot have zero distance to enough of its points to feel infinite force.
No, it's stronger than that. It says that any spherically symmetric distribution of matter outside a certain radius exerts no "gravitational force" on anything inside that radius, whether there is matter inside that radius or not.