I'm in NJ, a international student just got my graduate degree in Dec, and have been seeking for full-time job or intern in design & manufacturing related area for two weeks. I designed bevel-cylindrical gear reducer and have strong skill in 3-D CAD modeling, FEA, computer programming and optimization design, also knowledge of manufacturing process but without much experience. . . .
Seems to me your qualifications may already be about 20 or 30 years out of date? What gear reducers needed to be designed in NJ, might already have been designed. 3D Cad modeling and FEA were an unexpected bonus in a new employee two or three decades ago. Now, they're about as much a distinction as "can type fast and even take dictation" was to a secretary in 1970.
My point is that the industry you choose may be more important to your future than, say, getting a master's degree in FEA of gear trains or whatever. The US probably already has most of the engineers it's going to hire to design gearboxes, traditional automotive gear trains, to model or simply analyze someone else's designs, etc.
That you're here and have completed an engineering degree -- and actually like programming and optimization -- suggest you're bright. That's a plus -- you might be a quick study.
That you're an international student with a good but incomplete mastery of written English is probably a minus for many engineering firms -- but possibly a big plus for a firm with overseas clients or operations that could use dual-language proficiency. What is your native language -- and what company might benefit from your having it?
As just a rough guess of a direction you might head -- agricultural machinery still needs good mechanisms designers. I'd consider finding an international firm, in some still growing and relevant industry (ag and construction machinery, medical devices, process equipment, robotics, autonomous vehicles and aircraft, etc.) and look for a challenging job. Your background and skills should be good enough to get you a job designing something like agricultural or construction equipment implements -- and there's a reasonable future for that industry as well as global needs that might leverage your native language?
NJ (if you're set on staying near) has a large number of pharmaceutical industries -- and new drugs require a surprisingly large amount of automation from gene sequencers to process equipment for making the stuff.
Once you've found a thriving industry to get a start in -- you might choose a firm that will keep you on as you later decide what sort of Master's degree might help you advance in one of the growth industries of the future.