Ultimately, you'll be under-qualified in Poland. There are hundreds of people graduating every year with better qualifications than you - with the added ability to speak 100% fluent Polish. I've been involved in hiring people recently for some hospitality/tourism jobs - and we wouldn't consider anyone without complete fluent Polish unless they were an exceptional candidate. From what you describe - you aren't exceptional.
Associate of Technical Arts in Hospitality and Tourism
Not enough. If you want to get a job on the same basis as a Polish person, you'll need to have similar qualifications - which means a bachelors degree as a bare minimum, with most employers looking for a Masters for this sort of job. They simply won't care less that you come from a different educational system - you need to have the same as Polish people have.
I know this from recently recruiting some people - we threw out any CV's where the candidate didn't have a Masters degree as a bare minimum. And this was for a basic hospitality/receptionist job! It might seem crazy, but with 200 CV's to go through - there was no need to hire anyone without one.