I could have paid the citation fine online but I wanted to avoid points going on my license
Does your unidentified state not allow a person cited for a traffic violation to take traffic school?
it was suggested that I go to court to ask what I can do to remove the points.
Suggested by whom?
the other driver filed a personal injury claim
With the court? With his/her own insurer? With your insurer?
however, no one at the accident had any injuries. What are your thoughts?
Well...rather obviously, the other driver disagrees with your belief that "no one [involved in] the accident had any injuries." Equally as obviously, we have no insight into who is right.
Should I just pay the fine online and accept the points on my license (I plan on buying my car soon, so i want to avoid high insurance premiums) or should I go to court and plead nolo/ no contest.
When you rear end another car, there is virtually no viable defense. What do you expect to happen by "plead[ing] nolo/no contest"? Do you even understand what that means?
Nolo contendere (literally, "I do not want to compete" and commonly translated as "no contest") is a plea to a criminal charge that, in most states, is virtually identical to a guilty plea. A defendant who pleas no contest will be convicted just as if he/she had pleaded guilty. The only difference is that, whereas a guilty plea requires that the defendant admit to the crime, a no contest plea includes no such admission. It's as if the defendant said, "I don't feel like challenging the charge and will accept the consequences, but I'm not admitting that I did it." This distinction means that the victim of the crime cannot use the plea to prove liability in a civil lawsuit arising out of the same incident.
Thus, whether you plead "guilty" or "no contest" will likely have no bearing on "points" that you get on your driving record (of course, this is subject to the laws of your unidentified state). Assuming you reported this incident to your auto liability insurer, you should contact the adjuster and discuss this issue. It may be that the insurer will prefer a "no contest" plea for the reason mentioned, but it's also possible that the insurer won't care. Of course, you could also plead "not guilty," but you don't appear to have any valid defense. Finally, if your state involves prosecuting attorneys in routine traffic matters, you could try to make a plea bargain.