A few months is not long - allow yourself time before you ultimately decide whether you want to stay with him or not, keep in your head the option that you can leave if you want to - he's the one who needs to be making an effort. I think men sometimes think cheating is just 'sleeping with another woman' and that once they stop doing that things can start to get better. But actually it is so much more
There's the deception - all the times they lied to you - how easily they lied.
The feeling that thye may have betrayed your private life to the OW - talked about you, bad mouthed you whatever.
The fact that they deliberately and knowingly did something that they knew would cause you huge harm and terrible hurt, they thought about that but did it anyway.
That they were willingly to lose you (and wreck your family if you have children) so you know that ultimately you aren;t the most important thing in their lives.
It is that awful sick feeling when someone has betrayed you, that someone you thought was the person who loved you most has treated you so shamefully and nastily, without a care for your feelings. That is a massive divide the knowledge that they could do that terrible thing to you and takes a huge amount of getting past.
And of course there is also the sex with someone else, but for most women I've talked to it is the emotional more than the physical betrayal that is so hard to get past.
I couldn't get past it with my XH - I knew I wouldn;t be able to trust him and I knew that if we stayed together we would both be miserable - I wouldn;t trust him, he would feel watched and untrusted. It was broken beyond all repair.
You are entitled to as much time as you need to sort through your feelings, and if he wants to commit to your relationship he needs to understand and acknowledge that, to truly understand the depth of the damage he has done.
You say you are rarely nice - that's unsurprising - he was phenomenally horrible to you, you don't owe him niceness, you are trying to give it a go that's really more than he deserves.
I would aim for keeping things civil, in an everyday sense - so try not to argue about pointless things, but let him know that it will take you time to get through the deep anger you feel and he needs to be patient. Trust and respect has to be earned - it doesn't just return because he isn't sleeping with OW now. He needs to prove he can be trusted, and for me the important hting was that my X acknowleded and respected my feelings and actually 'got' how betrayed I felt. sadly he never did and we went our separate ways.
I hope things turn out better for you, but don't be told what you are allowed or not allowed to feel, listen to your feelings and allow yourself whatever time you need to work through them - there aren't any rules about how fast it has to happen (or if it happens). And you may very well find it is one step forwards two steps back for a while - its not a smooth road.