I agree that the vet should be able to help you out. I was told by a vet that Iggy was not doing anything unusual and it would only be a problem if she was laying eggs a lot, not just a few random ones like she was doing. I was given some great tips on what to look out for and when egg laying becomes too much. I really prefer to have my females lay zero eggs because I hate worrying. It is one of the big reasons I am unsure about getting a female Eclectus, though I love them.
My female cockatiel Iggy came to me with the inclination to lay eggs occasionally. She had been the only bird at the house of the lady who rescued her (who was a really wonderful person that helped so many animals) and would lay eggs anyway.
I did not take the eggs out after she laid them because I did not want her to lay more to replace them. I made sure she always had a cuttlebone and gave her eggs more frequently than usual. We had one scare where I thought she had an egg stuck (she was just teasing me it turned out) and we almost went to the Animal Medical Center in the middle of the night. I was hysterical and did not find it funny at all but she seemed to think it was hilarious. I think she enjoyed the attention. She is very smart, sometimes too smart.
Her egg laying was never too much and I was not worried about her getting sick or dying, I just did not want it to turn into a big problem where she started laying eggs all the time. I wanted to do something preventive. I began a mission to figure out what I could do to make her stop once and for all. Funnily enough the answer was to move their water bowl. They have a very big water bowl that is wide and deep enough for them to bathe in. I moved it from the center of the cage to the corner she was laying eggs in and she has not laid an egg since. That was quite a while ago too. One time my boyfriend put the water bowl in another corner and when I came home she had shredded the newspaper in her special egg laying corner to make a nest. So I think it was all about that one corner because she has access to the other three corners of the cage and has never laid any eggs there.
I also have made sure to never give them anything that might be interpreted as a nest. No boxes, no soft huts, no coconut huts, nothing. My parakeets have a beautiful coconut hut they love but that is because they have never shown any interest in having parakeet bambinos. They don't have any hut right now but that is just because I like to switch it up from time to time. When the hut is in their cage they don't sleep in it or anything, they just chase each other all over it because there are three holes in the hut so they can zoom in and out at top speed. I've also caught them storing favorite foods in there for later! I also have a Meyer's that is still very young, under a year. I call him a him but really have no idea so if he pops out an egg I will know for sure!