Stepparent, you've done the right thing coming here and recognising that you need to see a counsellor. Don't wait though as you might feel a bit better and then think you'll be ok. Don't go to any unknown either, go to your GP and get recommendations, whether NHS or private.
I think you are facing two issues here. The first one is that you might very well finally be confronted with the fact that dream you were building in tainted. You fell in love, started a committed relationship, felt utter happiness with that person, and then you got the cherry on the cake, a baby. During this time, you could, as you say, tolerate the rest in the background. Now that you have all you've ever wished for, you subconsciously see them as pests that infect what would otherwise be such a perfect life (I don't mean it that badly, just for illustration purposes). As you admitted to yourself and here, you fail to like them from the start and you decided to hope that nature would do some miracle and somehow make you use to them. Unfortunately, and as you are now realising, this usually only happens with your own children, all the others, you have to put efforts, sometimes a lot of efforts into bonding with them to get to the point when you actually care for them. The longer you leave it, the harder it gets, and to make it worse, they are now getting at that difficult age when bonding is the last thing they want to do and actually want to 'de-bond' from their parents, let alone a step-parent who doesn't care for them. So you are now facing a much harder battle.
Add to this that you are a new mum and naturally experiencing for the first time tiredness like you've never before so your energy reserve is very much depleted and the things you could ignore before are now a you are finding getting much harder to tolerate. Then there is the fact that you are bonding in that overwhelming way parents do with their newborn. Even many new parents of their second or more children will experience that their elder are suddenly becoming a bit 'annoying' after they become parents again. I know I did, even though I never stopped loving my eldest just as much.
If you continue as you are, you are going to put your partner in an unsustainable position. He loves all his children and you, but will find himself stuck in between trying to make everyone happy, knowing deep inside that he can only make one happy by making the other one miserable. It's a horrible stressful position and the stress usually do end up too much.
So do go and see a counsellor/psychologist who can help you gradually accept these children in your life. You don't have to love them, you don't have to parent them, you just have to accept that they are part of your life and that however unperfect they are, they deserve to be respected. Remember that we all start thinking our children will grow up to be just like we want them to be, ie. perfect in our eyes... they don't always do despite all our efforts, but we still love them deeply. That's how your partner feels about his children just as you might one day feel about your daughter too.