I suppose you could use yours, but I have a bit of a problem with the original in that addiction is addiction ... what might be getting worse is his physical and/or mental health because of that addiction. (I know – I'm not supposed to analyze these things.)
I agree with Copyright because it seems as strange to talk about getting more and more addicted as it does to talk about getting slightly addicted to a substance. It's a bit like saying she's "getting more and more pregnant" instead of "her pregnancy is advancing".
Maybe you can say "He's getting more heavily addicted..."
Thanks velisarius. Now I see there's something odd with the original sentence.
I can't use your suggestion for the paraphrasing because I have to use the word AND (and between two and five words).
I've thought of this one. How does it sound?