Could I possibly contract chickenpox even after I got the vaccine?

Yes. The cpx vaccine was found to be ~ 85% protective with one dose and >95% protective with 2 doses at least 28 days apart. Some that do get the illness after vaccination have a milder case or unusual pattern of blisters. The main selling point of the vaccines in the beginning was it's ability to decrease the frequency of death & hospitalization to minimal levels.