Can I just say that your English doesn't strike me as "caveman" at all?
It might be helpful to figure out where you are on the ILR scale for English, both for your reference and to know the right words for your resumé/applications.
At my company, I have hired and worked with ILR-3 (professional working proficiency) English speakers many times, with little difficulty. As long as you can speak and write the language well enough to do the job, it won't really matter too much.
There's written English and there's spoken English.
Not to discount Jacinto Jaimez, but written is much easier as you have time to proofread and correct. Jacinto might feel it's spoken English that's the issue.
I work in a company where most of the devs are eastern European and some but clients are western(North American, UK mostly). Some of the devs have lower intermediate English but it doesn't stop them from talking to clients.
And, generally, native English speakers are too polite to point out any mistakes. So, if you have some, non-teacher, native speaker friends/acquaintances and want to improve ask them to point out any mistakes you make. They'll, most likely, be happy to help.
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