Identify sick birds ? Wet wood pigeons

Hello I have a very active garden with wood pigeons , collared doves , robins ,tits , blackbirds, sparrows, starlings and a few hedgehogs .  I clean the feeders every 2-3 days and  change clean water daily .. I stock their food twice to three times daily /so small quantities at a time . 

I saw a wood pigeon yesterday really wet ( others looked dry in spite of rain ) he also had one eye swollen shut,  but otherwise eating and “being  the boss of the garden :) “ ensuring he ate like usual , flying no issues other than wet and one swollen eye . 

in spite of stickers on the window I think he may have been the wood pigeon that crashed into my window about a week ago . 

is a wet pigeon or bird always a sick pigeon or bird  ? ( I’ve seen woodies look wet before with no other issues ) 

When do I pull my food for two weeks under what conditions ? Ie describe what makes a sick bird viewing to pull food ) 

 Also I had a hedgehog rescue from the backyard two weeks ago could a sick hedgehog transmit disease ? 

I hate to pull food if the wood pigeon needs support after a concussion . 

I don’t have a large backyard to move feeding areas - live in Bicester 

Thank you so much lots of questions