Your last counsellor was unethical.
- She shouldn't have counselled you if she'd counselled your mum/knows your mum as your issues probably began in childhood and you need to talk to a totally neutral party. All counsellors know this is a no-no.
- Your counsellor should then not have used information from what your mum said to put you down in counselling. That was an awful thing to do and crossed all sorts of boundaries, undermining your trust and instead of supporting a development of your self esteem she would have known it would shatter it. It was cruel if I'm honest.
So your counsellor probably did much more damage than good - instead of building your self esteem and confidence in your own feelings she undermined them. I presume you've had a lifetime of this from family and relationships. It sounds like you're ready to stop feeling this way as you are starting to realise it is not you, but those around you that make you feel 'over sensitive'.
I would look for another counsellor via your GP, someone unknown to your family. Clarify it with the counsellor when you begin. Ask her what she thought of your previous experience and get that sorted so you can trust them.
They'll build your self esteem by looking at your past experience from childhood onward and allow you to reframe it in your mind so that you realise you were upset with people's actions in a normal way but that they made you think you were being 'over sensitive' when you weren't.
Then you can have the confidence to tell your dh to stop telling you it's your fault and man up. If he changes, great. If he decides to continue then decide if you can put up with it or not then. You will find that once your counselling starts to take affect, he will change naturally as he'll realise that you can't be put down so easily. Don't tell him what you discuss in counselling just incase he tries to use it against you.
Good luck and remember that you are not a rubbish mum. Like the rest of us, you are juggling all your commitments and to ask him for a little help at bedtime is totally normal. In fact, he should have seen you were struggling and come and helped before you asked. There's nothing wrong with carrying a tired child to bed. Both parents should be involved at bed time.