You're right, you'll never get total internal reflection in a sphere (seen from the outside). That's because of symmetry: a ray inside a sphere will hit the surface at the same angle at both ends, meaning that, if it exceeds the critical angle at one end, it would have to exceed it at the other one as well (and so would not have been able to enter the sphere from the outside in the first place).
However, you'll still get a lot of partial reflection according to Fresnel's law. It doesn't look like your code accounts for that, which is probably why your glass looks fake. Try including that and see if it helps.
(Yes, it means that your rays will split in two whenever they hit a refractive surface. That happens in reality, so you'll just have to live with it. You can either trace both paths, or, if you're using a randomized ray tracing algorithm anyway, just sample one of them randomly with the appropriate weights.)
Ps. If you don't want to deal with stuff like light polarization, you may want to just use Schlick's approximation to the Fresnel equations.