Can I claim myself as a fulltime student if I graduated from high-school and didn't go to college?

Yes, you were a full time student in 2021 if your school considered you full time since you attended at least 5 months. 

Yes, you were a full time student, for 2021, since you were in school for the first 5 months of the year. High School counts as a student, for tax purposes.  

Why are you asking?  What that usually means is that you were, most likely, still your parent's dependent for 2021.

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.

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
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 him self.

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

Furthermore, there is a rule that says IF somebody else CAN claim him as a dependent, he is not allowed to claim himself. If he has sufficient income (usually more than $12,550), he can & should still file taxes. In TurboTax, he indicates that somebody else can claim him as a dependent, at the personal information section.  TT will check that box on form 1040.

Even if he had less, he is allowed to file if he needs to get back income tax withholding. He cannot get back social security or Medicare tax withholding.

https://ttlc.intuit.com/community/dependents/help/when-do-i-have-to-answer-yes-to-being-claimed-as-a...

With the tax law change, effective 2018, most students will get the same refund whether they claim themselves or not. The personal exemption has been eliminated and the standard deduction increased. However, you only qualify for an education credit or deduction, if you are not a dependent.  But that statement doesn't take into account  the temporary Covid stimulus money.