question: how can you state you 'fully supported yourself" if you lived with your parents????? what does 'fully supported yourself' mean? did you pay market rent to your parents???? it may be to your (and your parent's) advantage to claim both of you on their return. For example, if you did not work, there is no child care credit, but for them their would be.
run through this tool and determine the answer to your question:
https://www.irs.gov/help/ita/whom-may-i-claim-as-a-dependent
go through it two times
1) answer the questions as if you were your parents
2) answer the questions as if you were yourself
