I had blood clots go to both lungs in October, and went home feeling really freaked out, knowing they were still there. After 6 months of warfarin, mine went away, and (knock on wood) haven't returned. In my case they never figured out where the clots came from. I still get chest pain where the clots were every now and then, especially if I do a lot of strenuous activity. My doctor said it's normal for pain to last since the tissue was damaged. Also, I had pneumonia at the same time, so that's why I have scar tissue that he says might take some time to fully heal. Also, usually patients are put on warfarin for at least 6 months because in some patients it does take that much time for your body to dissolve the clot.
That being said...you can get clots while on warfarin. It is more rare to get them on warfarin than to get them while not taking a blood thinner. My sister's friend is on warfarin and still gets clots every once in a while. She and her doctor are looking into another drug (don't know what it is as I haven't had to take it) that might help her better.
Are you seeing a hematologist about the clots, or who is treating you for them? Maybe you should talk to them to see if there is an alternative therapy (drug) that might work better for you.
32 yr old female-dx with Crohn's in '97 after emergency resection and appendectomy, 2nd resection '05, Bilateral pulmonary emboli 10/09
Currently on Humira, Omeprazole, Effexor, Seroquel, Calcium, Vit D
Coumadin stopped 3/15/10!!!!