As I understand, I can use 'myself' for example: 'I see myself in a mirror' and I can't use this word if I want to say that I did or I will do something without help. I should use 'on my own'. Is it correct? Thx a lot!
With regard to your sentence, on my own is a better alternative because there is nothing surprising about that. 'Myself' is used to emphasize something.
For example, I did all of the work by myself, here you are emphasizing that nobody else has helped you do the work. But when you say I do my homework on my own, you just mean that nobody helps you, and you don't need