Vectorise Logo – No Drop Shadows

I have a low-resolution raster version of our logo (embroidered) and I need it rebuilt as clean vector artwork. Please replicate every line, curve, exactly as it appears—no stylistic tweaks and absolutely no drop shadows... (Budget: $30 - $250 USD, Jobs: Adobe Creative Cloud, Adobe Illustrator, Adobe Photoshop, Graphic Design, Illustrator, Logo Design, Photoshop, Vector Design)