Hello! I would check a few things...
First your bow arm position. You may be straightening your arm too much at some point in your shot sequence. Sometimes archers with extend the bow arm to get to full draw without even realizing it... or you may not have good bone alignment and are locking your elbow. check these first.
Next, check your bow hand position and tension on your grip. Check out this target archery video on proper technique:
http://www.performance-archery.tv/?q=node/2 If all of those things are OK, then you are likely putting some kind of torque on the bow in your shot sequence. Try breaking the shot sequence down into its parts (pre-draw, pick a spot, draw, release, follow through) and see if the problem is in there. Try dedicating one day each week to each part of your sequence and practice only that. This helped me tremendously!!
If you have a shooting buddy, it helps to have them observe you as well to see if you are doing anything peculiar in your shot.
OH and target panic is more about poor groups and psychological shooting issues than physically getting string slap on the arm... Really, target panic is where worrying about how the shot will turn out impedes the ability to shoot well. I don't think you have that problem from your description... That said, you could develop a target panic issue b/c you want to avoid the pain of shooting if you don't correct your problem.
Hope this helps!