Can I get a lawyer for an accident where I didnt get injured?

The only way to reduce or avoid points is to go to court and either convince the prosecutor to dismiss the case or let you plead to a lesser offense, or go to trial on the ticket and prove at trial that you are not, under the terms of the law, liable. A lawyer will help you greatly in doing this, and lawyers will handle traffic cases for, in my experience, $750 - $1,500 typically. (I do this up in NJ and that's my fee range, for example.)
Note two things in regards to the ticket, however: 1) it doesn't matter if you think you were at fault or not--what matters is whether whatever you did fell under the terms of the statute under which they issued the ticket; look at the offense(s) for which you were cited and compare to your actions that day, to see if you should or should not be liable for those 4 points. And 2) in my experience, the court *always* believes the officer, so you (or better yet, your attorney) are likely to get a better result from negotiating with the prosecutor and trying to get a favorable plea deal than by actually going to trial.
As to getting money for your car damage/repairs: unless you have your own relevant insurance to claim under (e.g. collision coverage), the only way to "expedite" matters if no one is offering to pay you is to sue the at-fault driver (you sue the driver, not the insurer) and prove his/her fault in court, such as by your testimony, police reports, police offer testimony, other witness testimony, etc. If you can prove the other driver's fault, you can get a court order or judgment requiring him to pay (at which point his insurer may pay for him, if they don't choose to settle ahead of time). If the amount in question does not exceed the limit for small claims court, suing in small claims, as your own attorney or "pro se" to minimize legal costs, if often a good idea.