What do me and my child's mom have to do to give up my rights to we ageed that its best for her because of my current health condition

What point would that help? If you getn SSD your child can receive a supplement. Also if there is no order in place and she doesn't want to receive welfare or anything there is no point. What are you trying to accomplish? You can't just give up rights. Is she married now?

You don't... not until the child gets adopted by someone else... and it won't happen before that takes place.

There is this myth that a parent can just sign over their rights. But its only a myth. Only a court can terminate parental rights and courts are very reluctant to do so. They will only do so under specific circumstances.

And why does your health make it better to terminate your rights?