Not necessarily. The reaction indicates that your child had a very robust immune response, likely to the measles portion of the vaccine. A reaction to one live vaccine does not predict what the reaction will be to a different live vaccine.
The only caveat to this would be if he had an immunodeficiency or was immunosuppressed (via medications such as chemotherapy). It is doubtful that your son falls into this category without you being aware.
I'm sure that was worrying. As parents, it's frightening to watch your child have a reaction or illness. Your son's immune response is an indication that you made the best choice - if he had gotten full-blown measles, the response likely would have been a LOT worse.