OP I completely understand how you feel, my ds also found out his dad was having another child through an over heard conversation, he was absolutely devastated and tbh a year later he still is.
He has only met his half sibling twice and doesn't actually want anything to do with him, which is sad but the way exdp dealt with it was disgusting.
He literally never said a word to him even after ds had asked questions, it got ignored and was told to basically mind his own business.
Their relationship now is pretty much non existent, he doesn't have any over nights due to his partner (ow) being extremely jealous of me that she constantly harasses me to the point I had to get the police involved, so he only gets to see him when she is off doing her own thing.
He's also 42 and shes 26 
he never wanted anymore children, but believe me she was adamant and it may sound harsh but it was definitely to trap him as she thought she'd caught a prize, unfortunately for her he's still up to his old tricks and cheats on her too, but she is more than happy to stay with him.
He recently left her when their child was a few months old, begging to come back to me as the grass wasn't so green and our ds is much older and less reliant on either of us and the fact that he'd hot so used to me doing pretty much all the parenting, it was a big slap in the face for him having to deal with a new baby plus work and ds, he completely buckled.
I know it's hard but you will get through it, I still have the odd wobble and little cry but I look forward to mine and ds futures and am so happy to know that all the crap we've been through we're still much better off and certainly happier ex isn't really in our lives anymore and that he his living in hell and can't get out.