To be pedantic, tonsillitis is a condition, not a disease (in the same way that a headache or stomach pain is a condition and not a disease). It's usually caused by a virus but it might also be bacterial in its origins.
Because there are a variety of causes it's impossible to say how contagious your type might be. However, unlike colds (etc), I can't ever recall hearing of tonsillitis sweeping through a family. (I suffered with recurring tonsillitis for most of my teenage years, but I can't recall my parents or friends ever catching it).
More here:
http://www.nhs.uk/Con...ges/Introduction.aspx
(Click through the tabs)
Chris