Hi Sinead.
Sorry to be pedantic, but if one cannot be pedantic here, then where else? 'Might of' is incorrect. One could have the 'might of the Roman Empire', but you mean 'MIGHT'VE' which is short for 'MIGHT HAVE' The same applies to phrases like 'COULD'VE'. Again, 'COULD OF' could never be used.
i hope you don't mind!