Nah, that is not a sick deer, it is a deer that has been around people and has been fed by people. It is looking for a hand out. You see it is a bit jumpy because the people are strangers bit it still associated them with food. I have seen that before. That deer will not see another year.
A few years back, buddy and I were hunting turkeys. Sitting a few yards apart facing opposite directions. Spike came up to me , sniffing,head bobbin sideways looks ,sniffin my boots. Goes over to buddy doing same thing but as soon as he smelled his boots he bolted. A few minutes later a box turtle makes a bee line for me, fast for a turtle, goes around my feet to my buddy then pulls inside his shell and stayed there for an hour. Go figure.