Unfortunately, you fears are well-founded. That's because no vaccine is 100 percent effective.
To support this statement, there was a study reported in the Journal of Infectious Diseases about a measles outbreak in the Netherlands that involved several thousand people. Surprisingly, you were more like to catch measles if you were vaccinated and living in a highly unvaccinated community than if you were unvaccinated living in a highly vaccinated community. In other words, you were better off living in a situation where you were unlikely to catch measles (i.e., a highly vaccinated community) than if you were in a situation where your risk of exposure was great.