Penal Code 273.5(a) is corporal injury to a current or former spouse, someone you have dated, or the other parent of your child.
Penal Code 273.5(c) is not a separate charge. It is the part of the section that defines the sort of injuries qualify for a conviction.
This is a very serious charge. It can be a misdemeanor that can land you in jail for up to a year, or a felony that carries up to four years in state prison.
If convicted, you would also have to take a 52 week domestic violence class, and would never be able to own or possess a firearm. If you and your boyfriend had a child, it would also make it far more difficult to get custody if you ever broke up. It could also lead to deportation and permanent exclusion from the United States if you are not a citizen.
Butte County has a diversion program where a person can take the 52 week domestic violence class and get the charges dropped. I don't know whether you would be eligible for this class.
You need a lawyer, who is the person who should be preparing for the case, not you. This is not a do it yourself project.
From here on out, I would encourage you not to talk to anyone about the case but an attorney. If you can't afford a lawyer, you can ask the judge to appoint a public defender when you make your first court appearance.
My office is in Chico and I offer a free consultation.
The previous answer is detailed and correct. The ultimate xharge you face in court is up to the D.A., and they decide if its a felony or misdemeanor. This sounds like misdemeanor conduct, and with the mutual combat nature of it, a dismissal should be achieved with competent counsel. Hire someone that knows what they are doing!