Does a cop have to charge someone with assault/ battery on an officer or could the cop choose to drop the charge?

No. The cops don't have to file any charges on anyone. Once filed its HIGHLY unlike they will drop the charges. 

If they choose to file assault and/or battery on a cop. That person is 99.99.99% going to prison for several years. 

If the charges are drop down to a misdemeanor you're still in big trouble.  

if you assaulted a cop its a felony i doubt it will be dropped