Logo Vectorization for Merchandise Printing

I have a logo that currently exists only as a raster JPEG/PNG. I’m satisfied with its look and colours; I simply need it redrawn as a true vector so it can be scaled cleanly for merchandise such as t-shirts and mugs... (Budget: $10 - $30 USD, Jobs: Adobe Creative Cloud, Adobe Illustrator, Adobe Photoshop, Graphic Design, Illustrator, Logo Design, Photoshop, Vector Tracing)