Being dishonest, or not fully honest is a slippery slope and won't benefit you or the baby.
I really do feel for you but remember, your visiting health team is there to help and support you, not cast judgement. This was a mistake and intent means a lot. As long as you recognize that this isn't a risk you can take again then I don't think there's any need to keep it from your MH team.
If you were a single parent, OP, you wouldn't be dealing with the added stress of living with someone that you know can't be arsed to help you. I'm not saying it would be easier but I'm not sure you can underestimate the negative effect having a selfish, useless 'partner' can have on your mental health.
Aside from that, I'd be telling you that you're in for a shitty time fixing bad habits but it's absolutely vital for you and your son. Feeding to sleep is a habit that needs to break. Co-sleeping is a habit that needs to break, in the short term at least.
This unfortunately means lost sleep, crying, disturbance. It's not fun and I feel sorry for you but I do think it's vital.
What I would say is that if this means you and baby staying in PJs and taking los of naps in front of the TV for the next couple of weeks then so be it. That's still better than you biting him or otherwise harming him in the night. It's not ideal but it is what it is.
My GP many years ago told me two pieces of old-school advice that saved my sanity.
- A crying baby is not the worst thing in the world. No baby ever died of crying.
- If you need a break, take it. Put the baby on the floor/in a playpen if he's mobile, and take your break. A baby can't fall off the floor.