You can complete the FAFSA for the upcoming school year until June 2022 as long as you get the whole process done before your school deadline to do so (which is usually well before the academic year ends).
However, the FAFSA really is used to determine the awarding of federally funded need based aid. If you are eligible for a portion of the Pell Grant, you will get it. You will also be able to take out the federally funded direct loan.
WRT institutional need based aid…the deadlines for applying for that have passed for most schools. But contact your college to inquire about this.
Also, does your college require the CSS Profile or its own form? Make sure you complete everything.
Federal Work Study funds are limited for each college. It’s very likely that those have all been awarded for the upcoming school year. In addition, work study funds are awarded to students who have financial need. Since you are full pay at this school (didn’t apply for aid) that implies you don’t have financial need. Is that the case!