The first thing to do is to split the birds up. It’s not a good idea to house different species together, unless you have a really large walk in type aviary. While they may do well initially, once hormones kick in, the smaller birds often pay for it. A cockatiel can kill a budgie very quickly. I would put the cockatiel in a new cage, and this might help break her breeding cycle. Female cockatiels are notorious for becoming chronic egg layers, whether there is another bird around or not. There are steps you can take to discourage egg laying, but if she continues, you have no choice but to take her to an Avian Vet for a hormone shot or implant. She will literally keep laying eggs until it kills her if she gets stuck in an egg laying cycle. Once you split them up, limit her daylight to 8-10 hours by covering her cage early each evening. If you put her in a new cage, this is the best first step. Regardless, rearrange toys and perches in the cage every couple of weeks. Move her cage to another place in the room as often as weekly. Make sure it is in a busy place in the house. Limit offering any fresh foods to once or twice a week. Do not ever give her anything she can sit in – no nest, box, bird tent or hut, no large food dishes. When she tries to nest in one place in the cage, hang some toys in the way and move the cage again. Never give her anything to shred like paper or cardboard. Basically disrupt her cage any time you notice she is acting nesty or lays an egg. If she tries to use a food bowl, take it away and replace with smaller bowls. Hopefully these changes will discourage more egg laying. Even it if does, I would not house the two birds together again.
Thank you for asking Lafeber,