If you are looking to get into the construction industry specifically, you'll want to focus on learning Revit (and Navisworks while you're at it). CAD/CAM is still alive and well, but everyone can do it and there is a major industry push toward Revit that is not going to stop. If you call around, the first question anyone is going to ask you is "How are you with Revit". You want to be able to tell them you have it mastered, and actually be able to perform. If you are technicallly savvy and understand automation & programming, you can separate yourself from the pack.
Most classes are going to be generic and indirect, teaching you some good basics, but not really preparing you to go out into the workforce and be competitive in a real work environment. Like most any career, you are going to learn a lot via on the job training. For that reason, it might be hard to enter into the workforce in a remote setting. If you can pick things up quickly and roll with the punches, you can do it.. but you may have a hard time finding opportunities without experience, as a lot of firms will prefer on site training when you are new. In that regard, getting in as a designer at an engineering firm would probably be your best bet.
Never stop learning. Jobs are sent to India every day, you have to give them a reason to keep one of them here for ya. Feel free to shoot me a PM if you have questions.