Question: Is it possible to tell whether you’ve been infected? I know there are some antibody tests out there, but I’m curious if there is a way to know whether you have vaccine-derived antibodies vs antibodies from an infection? 

Answer: First a reminder that FDA and CDC do not recommend using antibody tests to assess immunity (see Q&A of 9/7/21).  Next a direct answer to your question: Some types of antibody tests will not detect vaccine-derived immunity, but could detect infection-derived immunity. These types of tests are nucleocapsid antibody tests.  If you were curious to know whether you have antibodies from previous infection, you could ask your doctor to order an nucleocapsid protein antibody test (an approach that labcorp describes, here; note: labcorp is but one of many different testing providers and my mention is not endorsement).
As FDA describes, “currently authorized COVID-19 mRNA vaccines induce antibodies to the spike protein [S] and not to nucleocapsid proteins [N] that are likely detected only after natural infections. Therefore, COVID-19 vaccinated people who have not had previous natural infection will receive a negative antibody test result if the antibody test does not detect the antibodies induced by the COVID-19 vaccine.”