Birdie laid an egg and...

This is a prolapse and is considered an emergency, and needs treatment asap, this is a result of constant egg laying. If you cannot find a vet she will die, try contacting a wildlife rehab/rescue facility or a zoo, there may be someone there that can assist, or find an exotic vet. Are you in Nova Scotia if so try this place https://nicelocal.ca/nova-scotia/vet/type/treatment_of_exotic_animals/
The exposed tissue should be kept moist using a sterile lubricant such as Surgilube Surgilube Surgical Lubricant | Made in the USA

They would assess the severity of the prolapse and clean and reinsert the tissue and if needed put in a stitch or 2 to hold things in place, give her pain meds, anti inflammatory meds, antibiotics, calcium, perhaps fluid under the skin if she is dehydrated and possibly tube feeding. This is very serious, please do you best to get her some help. Maybe if you contacted someone at this link they could refer you somewhere Home | Nova Scotia Veterinary Medical Association

Call any vet and ask if they can refer you to someone, you never know who they may know that could help.

So sorry, thank you for updating.

So sorry for your loss, make sure your give your other bird extra love and attention.

Your other bird looks to be a female also.

Some females will lay infertile eggs even when there is no male around. I would suggest getting another female so you do not have to be concerned about unwanted breeding. Anytime you bring a new bird in you should observe quarantine rules and there is never a guarantee that two birds will get along if housed together so you must also be prepared to house them separately if necessary.