I don't think that I can improve my English any further.
I don't think my English skills will get any better.
I don't think my English skills will progress any further.
To improve" means to make something better than it was before. We can improve an object, and we can improve our skills in something. "To progress" is another way to say "to improve". It means "to develop towards a more advanced level".
"To improve"(良くする/上達する）とは前よりも何かが良くなる/上達するというような意味になります。
何か物を"improve"（よくする）ことも出来るし、何かのスキルなどを"improve"（上達する）ことも出来ます。
"To progress" （進歩/向上）とは "to improve"のもう一つの言い方になります。
これは"to develop towards a more advanced level"（もっと上級レベルに発展/発達する）という様な意味になります。
I feel like I've hit/reached my limit and won't progress any further.
I think I've reached my potential in English.
When we say we have hit our limit, we mean we don't see anyway to progress, either from exhaustion or we feel like we aren't competent enough. A more formal expression is 'reached my potential' - you don't feel like you will get any better, you have done the best you can.
we have hit our limitとは、何かが尽きたり、十分な能力がないと感じたりして、それ以上進歩していく先が見えないことを意味します。
よりフォーマルな表現は、 'reached my potential' です。それ以上よくなる気がせず、全力を尽くしたということです。
I feel I have reached a plateau in my English learning
After a period of rapid learning - as when first acquiring a new language -there may be a period when improvement is not as quick or noticeable as before. This is known as a 'plateau' in your learning.
I am unsure that my English can be any further improved.
This expresses that you are doubtful about whether or not your English level can improve. From here you can explain to your teacher why you think that is, whether it be that you have studied English for many years or you are not strong at speaking or whatever reason you have.
I hope that this helps :)
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