"I want to improve my Swedish."
Translation:Jag vill förbättra min svenska.
You're thinking of the adjectives. I was using the nouns "Svenska/Tyska", which refer to the languages themselves, instead of things that are "Svenska/Tyska".
However, even as an adjective, you couldn't say "Min svensk".
Possessive pronouns always take the definite form of adjectives, so you would always say "Min svenska [noun]", "Ditt tyska [noun]", etc, and never "Min svensk", "Ditt svenskt".