Thank you Tilt for your answer, but I would like to have a native's confirmation because I have often found it in lyrics, so I guess it must be at any rate very colloquial and I have heard it from an American friend in casual conversation, so that I wanted to check whether it would be accepted in that context.
I am sorry to contradict tilt, but these formulations are both correct in AE, and they do indeed mean what Moon Palace thinks. The second might be more common than the first, and both are a bit informal and perhaps also a bit dated.
The expression "it does a body good" is very much present in the American ear... indissociable with the slogan from a long-running dairy industry advertising campaign.
I agree with you jann, even if I more often see it as "it does me a lot of good" than just as "it does me good", it certainly exists. And not only in the USA, for years people in Ireland have tried and make me drink pints of stout (you can guess the name of it all by yourselves) by saying it would "do me a lot of good".
Otherwise, if the context allows it one can also opt for something in the line of: writing helps me heal /feel better. Writing is good for my (mental) health, ... and all the variations made possible once we know if that feel good factor is linked to an illness (recovering from one) or to a personal pleasure/satisfaction.
Come on Tilt, be assured that your ability to withdraw your remark does you a lot of good indeed and I do hope you will keep contradicting me often enough, because questioning our certainties is what we need to move on.
Pour en revenir à l'expression "me fait du bien", je pense que la solution de Tilt est la bonne : makes me feel good. C'est plus près du sens et du niveau de langue que "does me good" ou "is good for me".