Hi OP.
Early breastfeeding is so hard. If you haven't been advised by HCPs to offer formula then it's not necessary. Your milk will come in faster and your supply will increase faster if you stop giving it.
While you're feeding tonight, Google the "safe sleep 7", then first thing in the morning set up your bedroom so you can bedshare safely for at least a week or two.
He needs to be with you and on your breasts as much as possible. Him in just a nappy, you in just pyjama bottoms, pop some boxsets on and shove your nipple in his mouth every time he moves.
Breastmilk digests really fast, and his stomach is the size of his tiny little fist. He will feed minimum every three hours for a bit.
Once your milk has come in he'll settle down a little, and then he'll up the pace again for growth spurts, or when he gets poorly and so on.
Your job: feed the baby.
DH's job: feed you, make sure you have lots of water, hold the baby so you can shower and change, maybe take the baby for a walk in the pram so you can sleep for an hour in the morning and again in the afternoon.
If he can definitely stay awake, wake him up and get him to watch you hold the baby while you sleep for a couple of hours tonight.
In a couple of weeks this will just be a blurry memory. You need to snatch bits of sleep where you can, eat well, stay hydrated.
Mine both fed hourly at this age, the eldest we did topups and my milk came in on day 8. The youngest didn't have topups, milk came in day 4.
because it's tough, I know.