Unfortunately, although it looks like your boyfriend has the edge (calculators suggest you ovulated around July 8 - 10), you can't be entirely sure and will definitely need to get a DNA test when the baby is born.
I think with it being so close it wouldnt be possible to tell, maybe try using a ovulation calender or conception calender it might give you more of an idea.
The 23rd/24th of July and yes they're regular
Hi when was your period due exactly and are your cycles regular, I'm in a simular situation myself an I understand your worry.