Hi,
What would be really nice is to have a copy of your relatives adoption decree. My adoptive parents had a copy and I would bet my natural mother had one also. In that decree, my natural mother's name was listed and my birth name. The paper was in the lock box so I found it when I settled my mother's estate. See if you can find such a paper. It should be about 3 pages of legal size paper in a blue cover and may be folded like a insurance paper. Check the Republican Nonpariel for any hospital listings for the date of birth of your relative. Check also surrounding newspapers ie Grand Island. Are there any other relatives that may be able to share information? None of mine were anxious to talk; neither adoptive or natural. Register with adoptives in search. It has been so long since I have done this that I have no addresses. There are registries out there where natural parents and adoptive children can register and may be you can get a match that way. As I think of other things that I did, I'll let you know. You may even check high school year books and see if any one has any likeness to your relative. Almost nothing is too far fetched to give a try.
Good luck and I wish you the best and I will stay in touch