If you feel good enough to begin running, then you need to go to a cardio rehab. The issue is not the possibility of damaging the new valve; but rather developing a irregular heartbeat by exercising too hard too soon.
One of the outcomes of heart surgery is that you heart reacts to being 'handled'. Literally, the organ has a pattern of responses to being picked up and pushed around during surgery. One of the responses is to develop an irregular heartbeat. This consequence is more likely to happen if the heart is unduly stressed too soon after being shocked by the trauma of the surgery. If you get an arrhythmia at this stage of your recovery, you are going to be put on betablockers and you'll kick yourself for being so stupid.
At the rehab, you are monitored w/ an EKG while you begin to workout. I started my rehab at 5 weeks post op. Towards the end of the second week I was beginning to jog... well more like the old man shuffle. By the third week, we knew there were no irregularities in the heart rhythms.
However,we still staged the effort levels using heart beats per minute. The initial limitations were 130 bpm at the first level; then a week later we raised it to 135-140 bpm, until about the fourth week, when I was cleared to push 145 and hold it there. By that time, I was limited by other factors like breathing and muscle tone; but not by the heart valve itself.
Running by yourself, w/o monitoring your heart rhythms, within the first two months is risky. I am at seven months now, and my run/walk is completely different than it was at three months. I fully expect to morph back into running within the twelve months post surgery, but I am very grateful to have begun using cardio rehab and would advise anybody who feels like you, to also begin your recovery in this fashion.