I'm so sorry to hear this.
When my marriage was in crisis, my ex wouldn't agree to relationship counselling until he wanted to end the marriage. For context, he said he was bi, then six months later that he was probably just gay, then in counselling that I was the problem. In the bi phase, he said we didn't need counselling. After saying he was 'one wife short of gay, or probably just gay' he agreed to counselling to save our relationship. When we got in with the counsellor, it quickly became clear that there was no hope. I think he didn't have the guts to tell me he wanted a divorce by himself, and thought that the counsellor would help him do it. He then proceeded to tell me all the reasons why he couldn't be married to me, which were all to do with me as a person and apparently his sexuality had 'nothing to do with it'.
We continued to have counselling together for a year 'to help us communicate through the change'. Whatever you do, don't make the mistake I did of sticking with it. It was 50 minutes of pain, stress and anxiety every week.
I also had individual counselling and that was what I really needed.
In fairness, the sessions together showed me what kind of a person he really was and did sort of help me to see that I shouldn't want to be married to him anymore anyway. Unfortunately, it sounds like your H, like mine, sees it as an opportunity to tell you what he thinks is wrong with you. Please don't let him do that.
You can self-refer for NHS counselling and there may be low-cost services in your area, but there will be a waiting list. Find someone who is on the BACP register for yourself. That is where you will find your safe space to sit with and process what is happening. Try a few different counsellors if you need to, until you find one who works for you.
Good luck. It's absolutely horrendous when you're in that state of early shock but I promise you won't feel like this forever.