Just to be precise -- You do not have a date of birth, nor a date of death. A date = a specific day.
If you had dates, then, yes, there are databases that can be searched by specific birth dates and death dates.
You can try looking for possibilities in these Texas and Oklahoma databases, but without more info, this will be difficult:https://ok2explore.health.ok.gov/App/BirthSearchhttps://familysearch.org/search/collection/1949342
Other things to try: Trace where your mother lived and try to find newspapers that may have announced the birth. Talk to any of her living relatives (cousins?) or friends that might know something.
It's also POSSIBLE that she had the baby before she was married.
It's also POSSIBLE that there's a mistake on the record.