Is it possible for me to get mumps even after being vaccinated?

Yes. Unfortunately no vaccine is guaranteed to work in 100% of the patients 100% of the time. But still well worth doing!
Yes. Yes it is possible to get mumps after especially just one vaccination. Even after 2 vaccinations some people may not develop high enough antibodies to prevent an infection. But with 2 vaccinations the chances of getting mumps drops dramatically. Have your doctor check your titers.