You may be able to get this charge (or charges) dismissed but I think you need to speak to an attorney in person before you get your hopes up. I have had several clients with these kind of charges who tell me that from their perspective the situation is just the result of a miscommunication only to find out that victim is saying that an assault did occur or harassment did result. It's impossible to know what she is saying you did, though it likely involves the emails and the attempt to contact her at work. Understand that an assault family violence case is a Class A misdemeanor carrying up to one year in jail or up to 2 years of probation and a $4,000 fine. (A harassment charge is a Class B unless you have a prior conviction in which case it is a Class A offense.)
If you don't have a lawyer already, you need to start speak to some local criminal defense attorneys ASAP.