What a stressful morning!

Well I don't know how it's done in other places, but I would never pick a chicken up by its feet. 

When a chicken is being held upside down, it can regurgitate the contents of its crop and then inhale it.  I read a very sad story recently of someone who held her chicken upside down  to treat it for lice, and this is exactly what happened.  Effectively it "drowned."  Of course she felt terrible and advised everyone not to hold a chicken like this. 

I've had a very kind vet explain to me the best way to hold a chicken - scooping it up with your hand under its chest, legs held firmly between your fingers.  Then you can tuck it under your arm and hold it securely without it flapping. 

I had to do this twice a day for a while, to give medication to a sick chicken.  Once you've had a bit of practise it is very easy and very calm for human and animal.