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.
If you've got it, I think I'd use it! I mean, most of us just suffer through the extreme exhaustion that comes with PEs. If the oxygen will help lesson it, why not?
In my experience, pushing yourself too hard can cause symptoms to flare up or re-occur (even if they've been gone for a while). Now is definitely the time to take it easy, indulge in the oxygen to help with healing, and tackle a few things on your to-do list that don't require being very active (e.g., calling friends and family you've lost touch with, reading magazines, catching up on movies you've been wanting to see).
You will get better over time... it just never happens as fast as we want it to. (That's probably the only guarantee about recovery, actually!)
As TNT said, pushing yourself can make things worse. It's very frustrating not being to do thing like we're used to. I never felt old till I got hit with the PE's. It's a tough thing to go through, but over time you'll notice improvement.