We pay child support on the 15th of every month and live in GA. The child turned 18 in Feb. We continue to pay child support while she is enrolled in secondary school(which is high school). My question is does child support run from the 15th-15th or the 1st -30. She will graduate 29th of may.

Depends on your courts papers and agreements that have been reached. Many agencies figure it yearly and slice it up to fit the pay periods of the NCP. So how yours is set and who it is paid to ( an agency or direct ) should be in your paperwork.

My non-legal opinion is that its your kid - splurge and pay the whole month regardless.

Other than that... I agree with Calif.