Pulmonary Embolism Support Group
By far the most common form of pulmonary embolism is a thromboembolism, which occurs when a blood clot, generally a venous thrombus, becomes dislodged from its site of formation and embolizes to the arterial blood supply of one of the lungs. Symptoms may include difficulty breathing, pain during breathing, and more rarely circulatory instability and death.

When I had my first bilateral PE in May 2014 I did a lot of sports. In fact, I had just ran a race the week before it happened (looking back, I should have given more attention to the shortness of breath I experienced that day).
I went back to exercise very gradually, first with some yoga and walks, because my HR would be very elevated even when I lifted myself from the sofa. Aftwerards, I progressed to very low-intensity weight lifting, and I went back to jogging three months and a half after my PE.
For me the main challenge, on top of elevated HR and shortness of breath, was the lung pain caused by lung inflammation and adhesions (still have residual chronic pain even now after almost 3 years).
I think you should just pay attention to how your body reacts to exercise. If your HR goes up too fast (and, most importantly, takes a while to go down again), take it easier and resort to milder forms of exercise. After my second PE in November 2015, I took 3 weeks off from exercise, but then started running almost immediately.
3 months after my second PE I ran my first half-marathon! It takes patience, but you will definitely get back to where you stood before.
Good luck!
Beginning in mid-January of this year (2017), I started feeling better after hard cardio days. I don't typically feel the effects of my workouts the next day anymore. I also don't get winded like I did at the beginning. I feel like I'm actually making progress cardiovascularly from my benchmark before the PEs.
I completed a half-marathon with my sisters in November of last year, but we just walked it to be safe. I'm running a half-marathon this coming weekend, and I don't think I'll have issues!
Good luck!