Negative self talk, while painful and damaging, can also be helpful and useful. It really depends on your outlook and approach.
how do I declare these negative thoughts okay when in fact they are not?
You are correct, the things you did and thoughts you had at the time will never, ever be "okay". But that's not what you're trying to accomplish here. You don't have to like or appreciate your worst thoughts and deeds (and I'd be terribly frightend if someone did manage to do so) but you do need to find a way to accept them as a reality that you cannot change, and moreover, you must not allow your mistakes to define you. It is common for a WS to begin defining themselves, to themselves, as cheaters, liars, betrayers. The thing is, that is not the entirety of who you are. Also, you need to understand that who you are, and what value you bring to this world, is largely if not entirely up to you to define, and to live.
You are ALREADY a better person today than you were when you were cheating. You are actively and purposefully working on becoming a better person. You are working on being more empathetic and caring. You are working on being an honest person, and showing your vulnerability. You've sought help, both here on SI, and via a licensed therapist. I assume a great many other things have chaged as well, perhaps your job, your friends, even family. And doing all that even when things at home are stressed, and yet you still find the energy and drive to keep working on it... that is the mark of someone who will succeed in being a better person.
So my long winded answer is, the way you learn to accept the things that have taken place, and then let them be part of your story. Not your proudest moments, no, but still, it is the truth, and it is your history. That history got you to where you are today, and it will still be part of your story 20+ years from now. Since it's in the past and you can't change it, that simply means that you don't need to expend work trying to do the impossible. You cannot make it go away. But you can be a better person moving forward. The very best way in the world to show how very sorry you really are is to take full culpability, and then take steps to become a better person. No one, not even the people you hurt, want to see you fail. For most BS's and family members, what they want to see is that you learned something from what you did, and grew from it. Because, until you do, let's be honest... you are still dangerous to your spouse. And they will continue to see you as dangerous, until you've proven to them that you are not. That is what you are working on now.
That seems like trying to give myself partial credit and not own who I am and how I act.
Not at all, I would agree with your therapist on this point. (I am NOT a therapist). This part takes some real courage and effort. In order to be a better person, you must first understand yourself, deeply. The things you did... why did you do them? What do you think led up to you being a person who cheated and allowed it to happen. If I went back in time and asked 5 year old you if he thought he'd grow up to be a cheater one day, what would he say? I doubt that was the plan at 5. So what happened? What made you desire someone else, what need did they fill for you, why did you have that need, and why did you not respect yourself enough to not let it happen in the first place? If you can't answer these questions then that simply means they will happen again, because nothing changes when nothing changes. So take your time, work with your IC, don't rush things, and yes, give yourself a little credit. Even if it's a pinch worth. Yeah, you fucked up. But that's over now. And the new plan needs to be the new and improved you 2.0.