I am/was self taught as well, mostly web-based to start with... PHP, then javascript, then C# over many years and up to using OO in all three. A year ago I started taking c++ classes in college and I can say I picked up a few very helpful things.
1. C++ gave me a look into pointers and how stuff runs at a lower level than any of the other languages.
2. Object use. I used objects before, but I didn't leverage them quite as heavily as I could have, including inheritance and polymorphism. What I learned in C++ has greatly affected how I code in PHP and C#.
3. One of my C++ classes was about efficiency in algorithms... so I learned a bunch about how stuff is done deep down and how to write efficient code. Very helpful for some of the stuff I do in PHP and javascript when working with large data sets.
4. Code design is a big one... before, I just put all my methods into a single class and called them there. The class ended up being more of a repository for functions and data than a real class. Now I have a better grasp of breaking stuff into parts and either creating child classes or whatever is appropriate.
It's still a learning process. I'm only on my 4th c++ class and haven't even taken the data structure class yet, but I've learned a tremendous amount, even in just the first intro to c++ class. My suggestion... take at least intro to c++ at a community college.. you'll probably be surprised how much you'll learn. As an added bonus, being familiar with programming makes getting an A a breeze, so you can concentrate on actually writing decent code and learning stuff.