"it [another language] is the second one I learned when I was born"?
No, not when. "Since" would work.
Well, here is the perfect way to write it!---> English was the first of several since ...
And "birth" does not even need to be part of it.
English was the second of several languages I have learned.
I consider English my native language as it is the first one I learned since I was born, as have my parents. English is my native language, and it is the language spoken by my parents. Nevertheless, my family has traveled a lot, and I hold nationality and citizenship in countries where English is not the main language.---This is good!