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.

Really, you're on an anticoagulant, so you shouldn't have any issues even if you do sit for a while. However, it's just a good idea to try to get some movement and activity in there. It'll help with stamina and conditioning after PEs and it'll make you feel better mentally.
Also, just a thought, but do consider going outside even if it is just for five minutes. I know the weather is awful... its been cold here too. However, I'm terrible about using weather as an excuse not to get any exercise. This past summer, I made myself go for walks, even if it was 90 or more outside (and I *hate* the heat.). The last couple of weeks, my husband and I have been going for walks, even in temperatures well below freezing. If the cold air bothers your lungs, put a bandanna or scarf over your nose/mouth.
Just taking a little control back will work wonders for you. Think about what you're comfortable with a go for it!
When I had my DVT, i literally would just walk to the garage and back to the house several times a day. My leg was too painful to do more than that but walking is important for your leg to recover. Then I started walking around my yard. And then I started walking down the block. Start setting small goals, ones that will not be hard to meet. That will help you stay on track and build confidence.
What are your thoughts on those little floor bike pedal devices? I know it doesn't flex the calves like how they say you need to do in order for the blood to flow upward, but wondering if it would help at all to do in small increments each hour or so?
I know it's cold out. It was minus 15 with the wind chill this morning when I took the dog out. Like I said, you don't need to go for a long walk right now. Just doing a quick back and forth outside or inside, even if it's across your apartment's parking lot. I think getting out of your apartment will help you mentally, even if just for a minute. I wouldn't look at it like you don't have enough room to do a big walk. To start, smaller, frequent walks at first is going to be better than long walks that may fatigue you or be painful.