Could a car accident add more problems to my posttraumatic stress disorder?

You are right on to recognize that the effects of trauma can be cumulative.  It is very possible that a car accident could lead to an increase in PTSD symptoms that were related to other traumatic experiences.

If you have been deployed to a combat area, you are most likely eligible for free counseling services through the VA Vet Centers.  The Vet Center clinicians typically have a lot of experience working with military trauma. Here's a link to a directory of Vet Centers:

http://www.va.gov/directory/guide/vetcenter.asp

Your service and sacrifice is greatly appreciated. 

There are many types of traumas, and they certainly can compound on one another as you experience them. Without treating the traumas, or incidents where you felt there was a significant risk to your safety or that of others, there can be a cumulative effect. What we have learned in the mental health field from studying traumas, is that the body as a whole responds to these stressors in order to keep you safe during the events. If the body does not realize that it no longer needs to respond in this way because the event is now over, and then receives a trigger from a new event, it makes sense that the new event could cause additional issues. Both of these events can be addressed with the help of a Counselor. There are many Counselors that specialize in trauma inside and outside of the VA, so shop around if you are able and find someone that you connect with. 

A car accident can be a traumatic event. Especially,  if it was serious, you could have feared for your life, felt everythingvwas out of control and had normal reactions to an abnormal situation afterwards. 

This may or may not be related to the traumas that you experienced in the military. If it is then it is possible that you will see a direct effect in triggering off PTSD symptoms. Even if it didn't, it is possible that the complexity of the two situations will interact inside you to be a combined response. 

Having already been diagnosed with PTSD, this might be a good time to reconnect with the help system you had around military experiences and explore it a little bit about the new experience. The right exploration does not have to make things worse and can be a good source of prevention.