I'm an Illinois adoptee so maybe this will help.
Assuming you are male, you cannot put your child up for adoption if the mother does not also relinquish her rights. The same is true if she wants the child to be adopted and you don't. It has been done in the past, but it is not legal because both parents have legal rights & responsibilities to their children.
If she wants to raise the child, you will be responsible for contributing support until the child is at least 18. If you are the only parent (say the child's mother is dead for example) then yes, you would be able to relinquish your parental rights or raise your child alone. Keep in mind that it would be in the child's best interest to be raised by an extended family member if it's not possible for either parent. The opposite is also true if you want to raise your child & the mother does not, she will still be responsible for contributing support.
Say that you and the child's mother both relinquish your parental rights and the child is raised in an adoptive home. You and the child's mother have no further financial committment to your child ever. You would have certain moral obligations to the child if they ever need to look you up later for medical or family information.
Have you tried to find one? It is hard because dr.s don't like to testify against each other. It's a club. Call the local bar association and get a list of malpractice lawyers in your state, and call all of them until you find one who will take your case. Good luck.