You poor thing. But. I am you. 12 years further on.
I have one DS aged 9. Conceived through IVF. We were living in Asia at the time and went to a clinic and because of my age, 36, the doctor agreed to try artificial insemination (I was totally honest about the reason). When they tested DH's sperm it was not great so doc advised IVF. I was lucky and got pregnant first time. DH is a great dad and adores DS. We tried IVF again but it didn't work and I couldn't face trying again. I did got through stages where I was very sad that we would only have one child but I have accepted it now.
We tried counselling but as we don't live in the UK it is hard. I do remember at one session though DH was totally honest and said it wouldn't bother him if he never had sex again.
I made a decision to stay with DH because I couldn't take DS away from him. We live in Hungary and if I were to leave I would go home to Dublin so it would mean a huge upheaval for DS too (leaving school and friends as well as his home and Dad) which I am not prepared to do.
Am I happy? Yes. I am. Once I made the decision not to leave for DS's sake and to a lesser extent DH's, it became easier. And although I sometimes miss sex I have gotten to the stage that it doesn't bother me too much. Menopause helping that I think.
Would I change things? Yes. I would have left years ago. Before I had DS. I SO know what you mean about the fear of leaving at 34/35 and possibly not meeting someone. That is what kept me with DH.
Unfortunately nobody can make the decision except you.
I think at this stage if I were you i would have an honest talk with your DH. And tell him you both need to go for counselling and that you KNOW he finds it very hard but that if he wants you to stay he needs to do it. In fact as others have said maybe start with the GP. A full medical to ensure that there is nothing physical causing it. And then proper counselling.