that image is very very blurry...hard to say what that is, but it could be a hernia.
YES, they make eggs if hormonally stimulated.
They can get stuck, and it can be deadly (egg-binding) or they can push too hard or have sexual contractions so often that they prolapse (w/or without an egg) or become herniated, so do look into this with an avian certified vet if at all possible.
This is potentially an emergency surgery situation IF an egg is stuck and the bird has been pushing hard enough to prolapse or get a hernia.
In a normal egg-laying situation, you do not normally see the swelling and redness etc. It could also be a tumor (benign or other) but based on the location, I am worried it's related to an egg, hernia or prolapse.
I hope others will chime in, but if at all possible, I would get your bird to the vet and in the meantime, keep things warmer in your house, and keep her calm as possible at home. If you use any head source, MAKE SURE it is not something coated in PTFE/PFOA/PTFE/Teflon...e.g., DO NOT just grab a random space-heater or blow-dryer (1. because these are often coated in chemicals that off-gas and kill birds, but 2) because they also could frighten your bird and counteract the calm you want to achieve between now and the car-ride to the vet's).
If no vet is available and things get really bad (and you know it is an egg) there are some VERY LAST RESORT tactics to hand extracting, but they can kill your bird...so only use them if you are already pretty sure your bird will die without intervention. If you are sure it is an egg, you can also try putting some coconut oil or olive oil on the vent, but my vet was hesistant when I asked him about that. I would try to get to a vet, keep the bird warm and calm, and oil the vent with safe oil if you can do so without freaking your bird out.
As a LAST resort, in the event that things are going down hill, that is when I would consider extraction (assuming you cannot get to a vet and bird could die without intervention)...AGAIN-- Only if you are sure this is an egg. They can break etc and that also requires surgical intervention to save the bird.
Hi,
I can't tell from picture. When did you notice this? And yes this is a veterinarian need situation. Egg binding can be life and death situation, if that's whsts going on.. vets will fid phone video consultation so worth checking. I can't tell , can you take another picture?
Added warmth is key for sick birdies https://vcahospitals.com/know-your-pet/nursing-care-for-sick-pet-birds
Went to a vet. It is a benign tumor. The expert said it is soft. It won't prevent her from making eggs but it would prevent her from breeding. The green male bird wants to mate with her. Thanks everyone. We have to drive over an hour to an exotic bird expert who can remove the tumor.