OP, is he caring and attentive in other ways?
Him wanting to spend time with you and not wanting to go out with others doesn't suggest the problem is a lack of overall love....
Is he very needy of you? Or do you think he is trying to keep you feeling central to him and is worried you will be down/ he's being a bad husband if he leaves you behind?
I am also wondering if he is a bit in denial about how sick you are? He's trying to pretend it's not there because he sent come to terms with it?
The other possibility seems to me that he thinks you have a better chance of being well if you don't let the illness limit what you do? That by leading a full, uncompromised life, you will feel better?
I think you need a good calm conversation with him about your illness and how you can both live with it well. Tell him that you've noticed he keeps asking you to do things, that this makes you feel guilty/ pressured/ can prompt worse health issues/ makes you worry that he doesn't want to be with you.... make a constructive suggestion (eg that YOU suggest activity when you feel up to it/ he accepts a 'no' when you say/ he goes out on his own and others.... that this, for you, would make you happy and feel like him loving and caring for you the way you need. Ask him if he needs something from you.
On the other hand, if he is uncaring of you/ oblivious to your needs in other ways then you have a much bigger problem.
Good luck!