You both certainly can "sue" each other for a variety of civil torts, but the real question is will you be successful in your litigation. This sounds like a "mutual combat" situation. Generally speaking, if you felt threatened or harassed, your remedy is to call the police. Unless of course, your immediate safety was threatened, then you certainly have a right to defend yourself.
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Whether or not you have a viable case would certainly depend upon several additional facts:
1. That there was in fact a trespass.
2. That there was in fact harassment.
3. That there is proof of the trespass, and/or the harassment (e.g., a police report, witnesses, etc.).
4. That your so-called "battle wounds" were in fact injuries.
Basically, you need to show that there is wrongful conduct on the part of the other party, that gives rise to a civil cause of action, that you were injured and that those injuries are documented and not minor, and that there are no defenses to your claim.
Finally, and just as important as all of the above, if you do sue that person and win a judgment for money damages does that person have the resources to pay that judgment? In other words, will you ever see a dime from that person?
First things first, if you engaged in fight and no one got arrested there is no criminal battery charges pending so far. Now, if a person chooses to sue for damages (medical bills, loss of normal life, disfigurment etc.) incurred in a fight with you, for instance, that becomes a civil matter and the burden of proof lies on the plaintiff (the suing party).
Can a person threaten you with a law suit? That probably happens daily. Will she? That remains to be seen. Consult a civil attorney if you are sued.
If you are arrested on a criminal charge in connection to the fight, remain polite, calm, do not make any explanatory statements, seek counsel on a criminal attorney.
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