I have a SQL database where I have a field that holds a date like
The SQL you are looking for I believe is:
WHERE STR_TO_DATE(column, '%m/%/d/%Y') BETWEEN STR_TO_DATE(column, '%m/%/d/%Y') AND STR_TO_DATE(column, '%m/%/d/%Y')
MySQL has a STR_TO_DATE function, which you can use to parse a string into a date object in MySQL. Then you can use the between keyword for comparison.
My suggestion to you is to store your dates in millisecond format. It will create a lot less confusion and hassle, and it is also a standard across many coding languages. It will also make comparing and converting dates significantly easier.