If a child has a sickness bug and is sick in the same room as me could breathing in particles make me ill? how likely is it to make me ill?

It depends: on the type of sickness the child has (respiratory vs. gastrointestinal). Respiratory illnesses are generally transmitted to other people by contaminated respiratory droplets, from a sneeze for example. Some viruses are much more contagious than others, and can live on surfaces (such as a glass or doorknob) longer than others.

Droplets: If droplets are coughed or sneezed close to you - there may be potential for spread of the infection.