Convert PNG Logo to Vector

I need my existing PNG logo replicated as a true vector so it can be printed cleanly on merchandise such as shirts and hats of every size. The design should look identical to the original—no colour shifts, font substitutions, or layout changes—just a precise conversion from pixels to paths... (Budget: $10 - $30 USD, Jobs: Adobe Creative Cloud, Adobe Illustrator, Adobe Photoshop, Graphic Design, Illustrator, Logo Design, Photoshop, Vector Design)