What happens if light/particles exceeded the speed of light for a particular medium?

Speed of light is indeed lower when light propagates through materials (as opposed to vacuum). This doesn't mean that individual photons go slower but rather that the apparent speed of light pulse is lower due to interactions with atoms of the material. So in this case it is possible for some objects to go "faster than light" and indeed very similar effect to sonic boom, called Cherenkov radiation, appears.

Note that for most materials the apparent speed of light is still huge (of the order of speed of light in vacuum) so you need very energetic particles to generate Cherenkov radiation. So this effect is mainly relevant for high-energy particle physics, astrophysics and nuclear physics.

There is a phenomenon somewhat analogous to an "optical boom" know as Cherenkov radiation which occurs when charged particles pass through a medium at a speed greater than the speed of light for that particular medium.

This produces a beautiful blue glow often seen in pictures of the cores of nuclear reactors. See the wikipedia page for pictures.

Not entirely sure if this answers your question but it may be of interest to you.