The fact that he has already filed criminal charges against you does not prevent him from filing a civil suit. If you can't control your pitbulls this is probably exactly what you need.
The man can file a civil suit against you even after you have resolved your criminal case. He does have a case but as he will have trouble proving any damages he will have trouble finding a lawyer to pursue this case. Be careful with those dogs - the next case could result in severe criminal and civil liability because you are on notice the dogs are aggressive. In any event, you are strictly liable for the damage caused by your dogs; meaning, no finding of fault is necessary to hold you responsible.
Was this a criminal case or a civil case? In either event, if he were to sue you for his panic attacks he would have to prove that he is actually having panic attacks, that he has sought medical care, and that he has other damages. Not an easy case to prove.
I do take issue with this statement "you are strictly liable for the damage caused by your dogs; meaning, no finding of fault is necessary to hold you responsible" - this is not always the case and it really depends on the law where you live and the specific circumstances surrounding the incident.
I do agree, however, that you need better fencing.