I'm going to break up with my ex due to my health issues
Why would you use your health as a reason to break up?
It's not that he doesn't care. He says that himself, but I'm reluctant to accept that.
I would like to know why you wouldn't believe him when he said that he cares? Dealing with your health issue alone can be tough and having someone who cares for you is essential. I would recommend you tell everything to him and I am sure that he will help you along the way.
I can't, I'm afraid that he will leave me.
I think that it is good that you are giving him the option though to deal with your health issues. I think that it is up to him though to decide what he wants to endure.