Vielka Cecilia Hoy, Founder/Director at Vielka Hoy Consulting, Teacher, and Parent
Hi there! FAFSA is going to give your college a summary of what you need. Next, your college decides how to distribute that money including how to distribute state grants (e.g. school scholarships, loans, grants, work study). If you find that FAFSA has calculated your contribution to be more than you can actually do, or if something happened between the time that you completed your FAFSA and when you are starting college, you should contact your college's financial aid office or bursar to make those changes (and FAFSA at some point to do the same).
Most of your loan financial aid is coming in the form of a federal loan. This means that the cap is set by them rather than your college. The federal government will say as a freshman, you can have X amount of Stafford unsubsidized, Y amount of Stafford subsidized, and so forth. So you may not be able to get more Stafford loan, let's say, but may be eligible for a parent PLUS loan or a private education loan from a bank.
Lastly, I would be super careful about taking more of any loan. Federal student loans stay with you forever and can not be discharged in a bankruptcy. So what may seem like only a few thousand dollars could turn into something really ugly ten years from now. Look at your budget for school and determine what you can manage in work study, a super part-time job (about ten hours per week max), or searching for scholarships that are still open now. Consider book rentals rather than purchasing, and other ways to manage budget items such as those.
So the short answer is yes, you should wait to see what your college is giving you because that will determine what external loans you can get. BUT you should definitely look for and apply to scholarships in the interim.