I graduated in March of 2020 does that count as a full-time student even if I was only there for 3 months in 2020?

Yes and no.

Because your time as fulltime student was less than (parts of) 5 months, you cannot be someone's dependent, under the "Qualifying Child" rules*.

But, since you were a full time student for a complete term (semester, quarter etc), you do qualify as a  FT student for other purposes, including tuition credits. 

*There are two types of dependents, "Qualifying Children"(QC) and standard ("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. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit. They are interrelated but the rules are different for each.

The support test is different for each type. The support test, for a QC, is only that the child didn't provide more than half his own support. The support test for a Qualifying Relative is that the taxpayer provided more than half the relative's support.

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