Hi.
He often rubs his face against chicken wire when he wants out could this be the cause?
Yes.
Your drake has - VERY probably - hurt himself because of your chicken wire, so I recommend you to prevent him from accessing to it
until you can replace it, or at least find a definitive way for your boy to not be able to be in contact with it again.
Regarding his wound... : do mix Apple Cider Vinegar with his water. At least for today. (Tomorrow too if you want to.)
You put one tablespoon of Appel Cider Vinegar per liter of water.
Of course use a PLASTIC waterer that is deep enough so your drake can wet his entire bill - nostrils included.
(Do NOT put ACV in a metal waterer, or you will
poison your duck!)
Vinegar will disinfect the wound, and
kill bacterias - thus preventing your duck's wound to fester.
...The wound is ugly, but not severe; so you don't need to worry about your drake.
Also if anyone knows what’s wrong with the redness on his eye that would be very helpful.
What do you mean, by
"redness"?
I can only see a red dot on his eyelid...
is it that?
If so : in my opinion, it could be a tiny wound or
just a blood spot - the cause then probably being your chicken wire,
again...
I would
not worry about it.
Your biggest problem is
really your chicken wire, that you need
very far away from your drake.
...Good luck with your boy.
Do monitor him, but do not worry excessively : he will be fine.