Poeni comes from Latin poena ("penalty; punishment"), which was borrowed from Greek poinē ("penalty, fine, bloodmoney") and is the source of English pain and pine ("painful longing").
What kind of "worry" is this? Is it to be anxious and to fret over things or to annoy and be disturbing.
In the particular case of'worry', could you consider accepting 'Do I need to worry', 'he needs to worry'. I appreciate that's not normally the translation of 'rhaid i', but in this case it is a lot more natural. ('Should I worry' as suggested below also sounds much better.)
This is only half a sentence, unless part of a longer conversation. In English we would not use "annoy" or "to be disturbing" in a sentence like this. You would never say, in English "Do I have to annoy" or "Do I have to be disturbing" That just doesn't make sense. So many sentences we translate aren't what you would use in everyday conversation. But it does help with grammatical construction.