Money doesn’t come from FAFSA. It comes from the schools themselves, and the $5.5k is a loan from the gvt.
FAFSA is a financial aid form which some schools use. These schools have a tendency to not meet full need. So you may need $20k in aid, but they give you $10k, leaving you with a gap.
FAFSA is also used to see if you qualify for govt help such as a PELL Grant or to enable you to apply for a subsidized loan.
CSS is another kind of financial aid form which other schools use. Schools that use this tend to meet your full need (the $20k in this instance) BUT they will require your dad’s info and will assume he is contributing to your college costs in their calculations. The only way for them not to include his income in their calculations is to have a waiver, but if he pays child support, I doubt you would get one.
Advice to avoid CSS schools is because they will include your dad’s income and expect him to contribute, even if he won’t. So in this example, if you were to include your dad, you may not get any aid with the CSS profile. A school using FAFSA may meet your need of $20k or not, but it won’t assume your dad is contributing.
I know: it’s complicated and confusing.
Schools that only use the FAFSA form: fill out the NPC on their website using your mom’s info only and see what the result is.
Schools using the CSS: fill out the NPC using both your mom and dad’s income (if as with Oxy, they don’t ask for each parent, add mom and dad’s together and enter the total)
Another option is to apply to schools that offer merit aid for your stats. Merit aid is available to everyone who meets certain conditions (stats, results, sometimes ECs/ community service) regardless of family income. Some schools offer automatic merit aid of various amounts depending on stats. Other merit is competitive and will require a separate application, essays and sometimes an interview.
Auto merit schools:
Alabama (check out the Blount Liberal Arts program)
Ole Miss
New Mexico
Miami OH
Arizona
Some Liberal Arts Schools also offer merit, but maybe not enough: Wooster, Denison, Suquehanna, Ursinus, Juniata, Allegheny, St Lawrence are ones we hear about regularly on here. In addition, several of these use the FAFSA financial aid form (see @Mwfan1921 's post above) and won’t ask for your dad’s info/contribution.
Kenyon, Grinnell and Oberlin also offer merit, but not as much as these less well known schools.