I am a shipt shopper and owe $101 in federal taxes. I then entered my 1098-T form since I am a full time student, and I didn't receive any deduction. Is that correct?

If the $101 is on line 17* of form 1040, it is self employment tax (social security and medicare tax), not income tax.  Tax credits cannot be used to reduce  self employment tax.

Students, under 24, are generally, not eligible for the refundable tuition credit**.

* Self employment tax  first shows on line 4 of Schedule 2, then transfers to line 17 of form 1040 with any other schedule 2 stuff.

**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. You cannot be supporting yourself on parental support, 529 plans or student loans & grants. You usually must have actually paid tuition, not had it paid by scholarships & grants.  It is usually best if the parent claims that credit.