I am a full time student in college, making roughly 20k/year, paying for roughly 90% of my own expenses (rent, utilities, groceries, gas,etc) can I file independently?

If you provide more than half of your own support for the year they can’t claim you. If you don’t, they can claim you but they can also choose not to. In that case on your return you would say that someone else can claim you but are not doing so. 

You don't mention your age. It matters whether you are under 24.

You cannot file independently, if your CAN be claimed as a dependent, even if they don't actually claim you.  In addition to your age, it matters who was supporting you prior to your August move. Yet another issue is whether your apartment is just for school, or have you  moved out, totally. 

There are two types of dependents, "Qualifying Children"(QC) and Other ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit, student status, a relationship test and residence test.

A child of a taxpayer can still be a “Qualifying Child” (QC) dependent, regardless of his/her income, if:

1. He is under age 19, or under 24 if a full time student for at least 5 months of the year, or is totally & permanently disabled
2. He did not provide more than 1/2 his own support. Scholarships are excluded from the support calculation. Student loans, in the student's name, are support from the student, unless the parent has co-signed. 
3. He lived with the parent (including temporary absences such as away at school) for more than half the year

So, it doesn't matter how much he earned. What matters is how much he spent on support. Money he put into savings does not count as support he spent on himself.

The support value of the home, provided by the parent, is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants.

The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf

See full dependent rules at: https://turbotax.intuit.com/tax-tools/tax-tips/Family/Rules-for-Claiming-a-Dependent-on-Your-Tax-Return/INF12139.html

Usually, a student wants to file independently to claim the generous American Opportunity Tuition Credit (AOTC) and/or because his parents income is too high to qualify for the AOTC. 

 A full time unmarried student, under age 24, even if you don't qualify as a dependent, is only eligible for the refundable portion of the American Opportunity Credit if he supports himself by working (more than half your support must come from your earned income). You cannot be supporting yourself on parental support, 529 plans, savings and investments, or student loans & grants. It is usually best if the parent claims that credit. 

You cannot claim the (up to) $1000 refundable credit if you are, or can be, claimed as a dependent by someone else.

Reference: Line 7 instructions for form 8863.

https://www.irs.gov/instructions/i8863#en_US_2024_publink53002gd0e674

If the student actually has a tax liability, there is a provision to allow him to claim a non-refundable tuition credit. But then the parent must forgo claiming the student as a dependent, and the $500 other dependent credit.  The student must still indicate that he can be claimed as a dependent, on his return. At $20K earned income, this is only worth about $540 to you.