I don’t think it suits. “Thick skinned” means you need to ignore criticism and keep doing what you are doing regardless. I don’t think that is the usual experience while learning another language. I think you need to deal with disappointment rather than criticism. A better sentence would be “You need to be determined if you are going to learn a language well”.
Thick-skinned means to not be easily hurt by criticism, so has nothing to do with being shy/introvert or outgoing/extrovert, and it definitely has nothing to do with speaking ability.
So yes, it would be weird to use it the way you said. (But wow, I wonder if my Mandarin will ever become as good as your English!)
As someone who has been involved in politics for nearly 20 years, I can confidently say that it is good to be thick-skinned in politics, but the vast majority of politicians are generally NOT “thick-skinned,” although people assume they are. Then tend to be thin-skinned, very sensitive, care very much about what people think of them, but have very high tolerances for pain.