I`m not a medical professional, so my advice shouldn`t be followed without consulting one. To the best of my knowledge you should NOT dive while still on anti-coagulants. Your best bet is to see a diving specialist after you`re off anti-coagulants so they can do a "ventilation perfusion test" to assess the damage to the aveoli in your lungs. Once again, not a medical professional but I`d guess the two biggest problems you could run into would be if a section of your lungs was weakened by the embolism and could rupture under high strain or pressure....or if part of your lungs has scarring now and could possibly trap pressurized air at depth and damage your lungs upon surfacing. Hopefully it all works out, but whatever you do, go see a medical doctor who is a dive specialist to make sure you`re ship shape!