Unfortunately being a mom with 3 young kids can be very stressful and it can play havoc with your milk supply. What might also be happening is that you are tense and that may reduce the let-down session when the milk is coming in. Make sure to wait 2 - 4 hours between breastfeedings - if he is thirsty, he can have a little spring water.
If you find that you're not getting enough sleep, you could try multi-tasking (we moms are great at that!) - take the baby to bed with you so that you can nurse him and sleep at the same time. Just make sure that the baby can't fall out of the bed and hold him football style - sort of like he's sitting beside you with your arm around him. You need sleep and you need time to yourself and time with your significant other. I know it can be difficult to find someone to watch 3 kids, but they are out there - get creative. A happy, rested mom is a good mom.
I hope things go well for you :) A.