Personal projects can work, but internships give you a foot in the door in a company. Do you know why you were not offered an internship? Perhaps it's simply because people assume that you want more money than the typical internship provides, but...

Since you're a mechanical engineer, you probably have a network there. Couldn't you ask one of them for an internship? Anything from an internship at a CNC builder to a custom system to organize drawings to a plugin for a CAD tool?