Hi AC,
I'm a new MNetter, but reading this thread made me think about some issues in my own life. I've always felt a bit ambivilent about sex (too much nice girls don't do that sort of thing from my mum), and felt some of the "why should I if I don't enjoy it" too. Dh sex drive rather higher than mine for a while, and mine really went down with two babies in 16months +breast feeding, lack of sleep etc. What I found I did was completely reject any physical intimacy, just in case it turned sexual and I had to say no, leading to unpleasant atmostphere. Then that meant he was sad and I felt guilty, leading to more avoidance of intimacy. Every now and then when I felt up for it I would pretty much seduce him, which I think made him feel a bit used.
All in all not good. We didn't talk about it for probably a year after dd was born, and it seriously damaged our relationship. We did the avoid accidental touching too.
Do you think your dw would be ok with a hug if you said that would be enough for you for now and there would be no pressure for anything more? I know it might not be, but in some ways I think hugs are more important than sex.
Do try councelling - even if it's just to have someone occasionally to really listen to you - I found it enormously helpful, and after my dh saw that I was feeling better about myself he did tentatively say he'd think about it too (nothing has happened yet, but you never know).
It is possible to live without sex (my parent have been celebate for years), but I don't think it's survivable in the long term to live without feeling cared for.
I'm sure you both would really like things to be different. Good luck!