I am trying to do the calculations on this.
If you are 23 weeks pregnant, you would generally count from the beginning of your last period, but since yours are irregular it's quite hard to tell.
If you were 5 weeks pregnant on the 23rd of November, you would have conceived approximately 3 weeks before that, on or around the beginning of November. So yes, unless I have counted really really badly, I would think it quite possible that you have conceived at this time.
Did you have sex with the person you are in a relationship around this time too?
If you only had sex with your ex around the beginning of November, the baby is likely to be his.