I need to improve my English

I am learning English because I want to improve in my work. My native language is Spanish and I could also help someone to learn it. ("could" is fine here.)

This "I am learning English because I want to improve in my work." is somewhat ambiguous. Do you mean that you want to improve the quality of your work or that you wish to gain a promotion for example?

If the former, then simply say "I am learning English because I want to improve the quality of my work."

Try to describe the improvement you seek.

I need to improve my English

I am learning English because I want to improve on my work. My native language is Spanish and I could can (use "can" rather than "could", since "can" refers to ability or factual things, I think) also help someone to learn it.