Relationships come in all forms, shapes and sizes op. In order to succeed, there needs to be honesty and sincerity between the two people involved.
He is being open with you. We hope!
Obviously we don’t know the context, which makes it hard to judge. Is his illness very serious? Why does he need anyone nursing him? Are you able to offer him the care and structure he needs in order to recover?
Ultimately I suppose, it boils down to whether you trust him or not?
But just as he has been honest with you, you need to be honest with him and say you feel uncomfortable and confused by this, and that you don’t know how to react, and see how he reacts?
If you need to step back for your own self protection op, then do so. You don’t have to play the role of cool girlfriend!
Tell him straight that you are trying to be understanding but you don’t know how to feel about this when the parameters of your relationship are so ill-defined. FWIW, I think that would be an entirely reasonable way to feel in these circumstances!
No one on here can tell you whether his closeness to his ex is a good or bad thing, because it could be either!
Edited to say that this situation is obviously a catalyst to seek more clarity if you are feeling confused and upset by these events. And if he is unwilling to offer that, then you may have your answer… .