A pigeon with a ruptured air sac will look as if it has a deformed but well inflated balloon under the skin. The swelling usually affects the head and neck region, but can also appear under the wings, sometimes simultaneously.
The bird's skin will be stretched to the point of being slightly transparent. It won't inflate and deflate when the pigeon breathes (this, if one sided, is a symptom of a canker nodule on one side of the throat).
If you press your finger gently on the skin it will dent, then fill up again when you remove your finger .
I have heard this condition describes as a pigeon full of air, a crop full of air (this can happen, but looks and feels different), and the incredible inflatable pigeon .
A small swelling can be left alone and will eventually repair itself ( a course of antibiotics such as Baytril or Synulox is recommended particularly if a cat or hawk attack is the suspected cause), but larger swellings will prevent a bird from eating and can press against the organs, so are better relieved if possible.
I usually advise people to contact a wildlife centre and ask an experienced person to talk them through the procedure on the telephone. Wing and a Prayer in Norfolk has done this successfully in two cases that I referred to them.
To deflate a large air bubble, use a sterile syringe needle if you have one, or sterilise a sewing or darning needle with a flame. Sterilise the area that you are going to treat, pinch the inflated skin together so that it makes a tent shape and gently insert the needle into the front of the tented area. Gently push the air out with your fingers.
The bubble will often refill and the procedure will often have to be carried out repeatedly. Keep the skin area clean and disinfected.
The pigeon will need to be kept somewhere quiet , on a clean towel in soft surroundings. Feed the bird small amounts of food, soft food is preferable.
If the bubble is a large one and keeps inflating it might be necessary to have a vet treat it by inserting a drainage tube which will allow the bubble to deflate continuously until the air sac repairs itself.
This video shows someone casually treating a ruptured air sac, it isn't as detailed and instructive as I would wish but should help.