no record of birth under my name

hi can you help......i gave birth to a child at the Providence Hospital El Paso around 2nd Feb 1968 have been into the El Paso births and there is no birth listed under my name Marion Bloise does the hospital have to give me my admission dates if I call or write to them to narrow the search i was in Jan27th to try to induce labor and went in again approx a week later thats why I believe around 2nd Feb although Feb 9th keeps comming to mind.....thank you Marion