Actually no, we are not married at all. We are planning for it.
This 'new woman' has been living with me for over a year. Oddly, our attraction for each other is not sɛҳuąƖ at all. Even discussed this with a priest in confession and he mentioned it's not a sin if we do not commit any acts but we need to be careful as we are putting ourselves in the near occasion of sin.
I have contacted my parish, asking how to go about getting an annulment for the previous marriage.
That is odd especially after a year or more. I have to wonder whether the two of you are suited for marriage (even if your first marriage was invalid).
As for living with her (as long as you don't commit any acts), I'm pretty sure a traditional Catholic priest would tell you that you should move out. I think your NO priest did not give you good advice, but it's pretty typical of the Novus Ordo presbyters.
After learning more about what is going on in your situation, I suspect that your struggles after baptism is God warning you that you need to remove yourself from this living arrangement (at the very least). Although we should expect difficulties after our conversion/baptism, I think it's odd that it happened right out of the gate for you.