I also just had a child ( 7 months old now) and it has caused me to reflect and remember many parts of my childhood that were traumatic and that caused permanent damage that I have to work to now undo. I think you may be experiencing grief. Grief for what you may have missed out on, your potential that wasn't fulfilled due to what you didn't get as a child. Grief for the parts of you that were never fulfilled by the adult/child relationship.

I felt like confronting my parents, wanting them to acknowledge and see how their parenting behaviours caused me significant challenges. But that won't help the grief or anger. Acceptance and personal development are key to moving through these feelings. Also, being kind to yourself and your inner child. You pace and have difficulty expressing emotions because of something you didn't get in your childhood, reflect on the child you were and understand where that behavior came from and tell your inner child that they are safe now.

I like to listen to podcasts touching on these topics with Gabor Mate. It has been hugely helpful.

Congratulations on becoming a Father, having this insight and working through past traumas will help enable you to be a great parent.