Does his ESA letters state you must tell them if any change of circumstances? The letters you get usually do, I know int if my mums friends moved into a care home and the husband had to claim as a single person because you aren't classed as being part of the same household.
I am totally unfamiliar about receiving PIP while living in a care home, Google says the care element should stop but mobility continue but if he's in a care home but the whole award should stop if it's a nursing home. Is he getting the full enhances for both? Is the PIP money being paid and managed by him or you?
You're supposed to let ESA know of changes yourself. PIP don't/wont always info share. The letters you get usually tell you that you must inform them of changes like decline in health, someone moving out or in and change of income etc.
My advice would be to get ESA claim updated asap as it's very possible he shouldn't be making a joint claim as you're no longer part of the same household. I'm not saying this to scare you, I'm only mentioning it because my Mums friend went through similar when her dh moved into a care home, they had to stop all joint claims and she had to claim seperatly as they were classed as no longer part of the same household.
Did/do you get carers allowance, you may want to check you've updated them too.
Have you informed council so that you're paying appropriate council tax?
I'd try not to panic or stress but I would get it sorted ASAP, maybe a citizens advice appointment to make sure you do everything correctly and claiming what you should be entitled to for yourself. It's a very confusing system and when someone you love is so ill it's very easy to overlook and make mistakes.