Well, your introduction tells me that you're half way there already. A lot of illustrators, like me, started out as graphic designers. The second part I think you could probably do on your own.
Start off doing simple logo marks and developing them into something more like the images you would find on a stock site, for example. Post some on here for critiques if you have a thick skin.
Developing a concept is not something one can learn outside uni I think, it's really down to following a brief and implementing it through research and your own brain power. Do some YouTube
tutorials, make your own briefs, start a sketchbook etc. Always start with pencil and paper. Your own personal style will come in time and experience.
It really depends what area of illustration you are wanting to cover, there are many. I can't think of any actual illustration principles that would differ from ones you would learn as a designer.
A lot of things, like creating an ellipse, for example, is often just down to trial and error and a good eye.
As for online courses, I did a quick search and found lots, so just pick one or two and try them out if not too expensive. Skillshare and Domestika are well thought of I believe.
