So overwhelmed

I'm doing this anonymous because I'm ashamed of all of this. My son is 9 months, me and. His dad have been on and off since I was pregnant, hes an ass. I wanted marriage, he didn't want it. He hasn't really been responsible at all, some weeks he comes around and wants to "make it work" then after 2 good days goes back to being an ass and just doesn't call or anything. For the past 2 months he hasn't helped me financially or anything in general. I am receiving Cash aid, even though I work full time, but only receive $100 a month for my son. His father hasn't paid child support in over 3 months. Yet he bitches and moans about me having him on it and how I'm trying to fuck him over, without the states help I'd be struggling so much more! He hasn't bought a single thing for my son in months, asks me what he needed but never bought it. He makes excuses as to why he can't see him, either he's tired or doesn't have a ride, but his mother called me a night that we were arguing to tell me he was drunk. It drove me insane how he had money to drink but not to come see his son. Fast forward to today, Easter, or was. He decided to go to a game with his family instead of spending our son's first Easter with us. His excuse was, he didn't want to go to church (which I didn't even require him to do) and that he wasn't going to change his plans after his brother bought his ticket (which was $9). He put his family before our son, as he always does. So he missed the first half of Easter. Called me till around 6 pm and asked me to drop off our son since he was finally free. I told him I was with family and that he could come see him instead in about an hour to two hrs. He never bothered calling back. I blew up his phone around 10 pm and never once did he answer or text me back. I'm so incredibly hurt at how little my son means to him I still have hopes that he will change but if his son, his own flesh and blood doesn't matter to him, how can. I matter to him? He doesn't try for my son whatsoever and I'm so ready to let this go, he won't play with my son's emotions like he did mine for almost 7 years. I think I've done my part as a parent and been fair and tried to make this easy on his dad, but there's always an excuse. Am I wrong for wanting to take full custody of my son? I don't want him emotionaly to mess with my son's feelings and make him feel unwanted , and only pop into his life whenever he feels like it. My sister tells me she thinks he has someone else on the side. I'm torn ladies my heart is aching not for his love but for my son. What should I do?