Unity is a great tool for hobbyists, if for no other reason than it saves you from having to build the framework for your projects, and lets you start making the game itself. I'm picky in that I want to have only and specifically what I think my game needs to be part of the framework, (and I wanted to learn DX11) so I've been working from the ground up, and I can guarantee someone working in Unity would have a lot more to show for their time compared to where I'm at.

As for C++: you've already made the biggest step (learning how to program) and have flexed those skills to great effect in your final project. I think you're in a prime position to use one of the "learn C++ through game programming" books, maybe keep "Accelerated C++" handy so you have a second opinion on how to handle certain things (since C++ has a lot of leftovers from original C, there are better and worse ways to do the same thing, like the ol' char* vs std::string problem). I wouldn't recommend trying to program games in C++ to a complete novice, but since you have several years experience with programming, it's really just going to be an issue of learning syntax and memory management. Having a few small games as testbeds for the language would be a great motivator for continuing to learn. I've made a lot more progress understanding C# while trying to make my framework do something specific compared to the sterile academic examples that books cook up for you.

As a side note: if you want to learn C++ because you want to learn it, by all means go for it. If you think it's what you need to learn to be a "real" game programmer...I'd suggest continuing on with the language you already have a couple years' experience with and look into some additional libraries if you want to add on to current projects. There's a .NET wrapper around almost anything these days.