If I signed a letter and had it notarized stating someone would take care of my child, am I giving up custody?

Custody is determined by the court. However, if you are leaving a child with someone for a period of time, the appropriate thing to do is to give the person power of attorney for a specified period of time and detailing what rights the person has as a surrogate decision maker for the child, e.g. to provide/sign for medical care, obtain school records etc. Otherwise, if the child is left long enough, the person can go to court on a 3rd party custody action. You should seek the help of an attorney to put together the power of attorney.