You are being silly, like seriously what the ...

He gets sick easily so of course he's gonna be "skittish" around sick people.  I'm in an office space and if i hear a sneeze during flu season i hide in my cube with a box of clorox wipes.

He is literally saying *i'll come over to see you if you want me too even though you're sick* and you decided to be passive aggressive.   
Also you said you like taking care of people, that's how you are and you don't expect anything but at the same time you expect him to read your mind when you literally told him you don't want to see him and not to come over.

I am soooo confused by your reaction to this.