No. Your return wont affect their return. And it would be the other way around. IF THEY CAN CLAIM YOU, you have to check you CAN be claimed. Why aren’t they claiming you?
Here are the rules for claiming a dependent. Do you qualify as a dependent?
https://ttlc.intuit.com/community/credits-and-deductions/help/who-can-i-claim-as-my-dependent/00/267...
IRS Pub 901 Tax rules for Dependents
https://www.irs.gov/pub/irs-pdf/p929.pdf
