A fledgling is a very young bird that has grown its first feathers. I wouldn't use it to describe someone's skill level (it's simply awkward), but you can use it as an adjective: "my fledgling English". Now you have the image of "my English": like a young bird with its first feathers, still waiting to be able to "fly". The last part of the phrase is not correct anyway: you can only say "in learning a new language" or "in learning languages".

This is not a complete sentence. What is the entire sentence?