Thanks for your question Tara.
Yes, you are correct about the egg laying behavior. It is very hard on a bird and they can die from laying too many eggs or becoming egg bound. Lovebirds are a species that tends to lay more so it will be challenging to correct.
I would not get another bird unless you want another bird. You are the one that will have to take care of it, pay for vet bills etc. There is also no guarantee that they will get along. Also, if you do get a male, you will just encourage her to lay more (regardless of whether there is a nest or not).
I would encourage you to remove the nest box or perceived nest areas to try and discourage laying. Right now, is she is still sitting on the eggs that she laid, I would let her sit on them for the normal incubation period (about 21-22 days). This will discourage her from egg laying again right away. If any of the eggs are broken or damaged, they need to be removed.
If she continues to lay, medical intervention may be needed. We can administer hormonal therapy which will stop laying for a period of time. In some cases, a bird will need to be spayed.
The other issue is to make sure your feed her correctly. If she is eating only a seed diet, she is at much higher risk of developing issues with low calcium. Your birds should be eating primarily a pelleted diet with healthy veggies like carrots, sweet potatoes, dark green leafy veggies. Seeds will become a much smaller portion of the diet. For more info see:
Please let me know what other questions you have.