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.
"Lazy people think of the easy way to do the hard stuff"