'An' signifies 'one.' In Middle English (think around the 1300s-1400s), 'an' meant 'one' or 'single' or 'alone.' The two words - an other - naturally join together in speech because of the elision between n and o, so eventually they were joined in writing as well.
Aince 'an' means 'one;' another means'' 'one other.' It would not make sense to repeat the 'an' (one one other is senseless).
'Other' would take a plural: do you have other jobs. Another means 'one other.' Do you have ONE other job - thus the singular. Since the noun in the Polish sentence is singular, that tells you that you need to use either 'another' or 'a different' in your answer.
In Polish, 'inne' means 'other' or 'another' or 'different' depending on the context and the number of the verb that follows.
I didn't try, 'Do you have other work,' but grammatically, that would work in English, since 'work' is uncountable ('job' is countable: a/one job, three jobs; but: some work; different work).