Fill popsicle molds almost 1/3 full with cooled, spiked tea. Freeze until firm, 60-90 minutes. Pour ~1 tablespoon of the peach mixture in to make a thin stripe. Add popsicle sticks now; freeze until firm, at least 60 minutes.
Repeat sweet tea layer, return to freezer for 60-90 minutes. Repeat peach layer, return to freezer for 60 minutes.
Fill molds the rest of the way with sweet tea, leaving about 1/2-inch of headspace. Freeze until solid.