It sounds like in your company you've done a nice training rotation into various roles a mechanical engineer might take on. Did any subject area of type of task appeal to you more than others? For example, a process engineer is likely to do overall system design, calculate energy, heat, and mass balances to achieve a system output. A project engineer would source the components or equipment needed to build the system and realize the design physically. You may also be interested in a project manager role, which would oversee such a project for a client, manage its scope, budget and execution to make a profit.
Often mechanical engineers favor the fluid mechanics and heat transfer side of the field or the more solid mechanics, kinetic motion, etc. side. If you have a preference, that may help narrow your search.
Mechanical engineers also work in many industries. Another way to source a new job is to consider what types of companies or products interest you. Environmental systems, industrial systems (and in what: power or steam production, environmental equipment, petroleum refining, oil and gas production, etc.), consumer products, materials testing and research, etc. Lots of ways to go in mechanical engineering (and yes, I am one). Good luck!