I think all triathletes should be made aware that PE seems to have a triathlon link. It seems that most of them can be traced to a clot that formed after a particularly hard race. Here is some advice from another PE sufferer:
- After every race, put on those compression socks for the rest of the day
- After every race drink and drink until you are going to burst a bladder…and do this before the awards ceremony (dehydration can contribute)
- Do a lot of walking/stretching before getting in the car for the ride home…it helps to make it a rule to wait until after the awards ceremony as this gives you a lot more time to ‘flush’ the legs before sitting.
- On the way home in the car, stop every hour and get out and walk for 5 minutes.
Women need to be especially alert because oral contraceptives are another risk factor.
And heaven forbid you are a woman on birth control, doing triathlons, who smokes.
In my case, I went undiagnosed for about 3 months, during which time I was still doing my best to race and train. I probably sustained more long-term damage than you did.
After they let me out of the hospital, I went back to swimming/cycling right away, but was told to hold off on the running (probably because I had enough clotting in my thigh to kill me if they broke loose). I got one emergency call that week from the nurse telling me not to do anything until further notice because my INR had come back at over 7 and I was at risk for bleeding internally.
Otherwise, I see no reason not to return to mild exercise right away. I think the best I ever felt was probably day 2 in the hospital…since then it’s been a continual up and down (1 year anniversary now). It’s a bit disconcerting that I will have good weeks and bad weeks still. But this is solely cardio performance, not muscular.
And in my case this is most likely due to permanent damage done to my lungs. I don’t know how much of my lungs are still working, but a lot of my lungs died from lack of blood flow. My body is trying to adapt (I have a 53% hematocrit), but I still suffer a lot when running and especially when swimming. The good news is I’m smoking fast on the bike. 
I may have lingering damage to my right ventrical from pulmonary hypertension…tomorrow I’m having a full panel of cardiac testing done just to be careful (I’ve been in a downturn).
As far as the coumadin is concerned, and assuming your INR will be around 3-3.5…I don’t see it having any impact on your cardiovascular performance. The only difference that drug should make is to decrease clotting…it shouldn’t change the blood’s ability to carry oxygen…and it shouldn’t have any other affect on other body tissue.
Your soreness is definitely caused by the time missed running. Ramp up gradually just for the sake of the legs. I wouldn’t do any zone 4-5 work for the next few weeks, but you can do all the zone 3 stuff you want until you reach that magical 3-4 week mark.
the main consideration, as far as I know, in regard to returning to activity is that the clots that are in your lungs and especially any remaining in your legs take time to dissolve and vigorous activity could contribute to lung damage in the case of clots remaining in the lungs, and another PE event in the case of clots in your legs that are dissolving.