As you may know (I suspect your doc has told you), DVT can kill. That's the bad news. One reason they're hesitant to release to activity is, often, a diagnosable DVT is often just the one they found; the fear is that your blood has developed a tendency towards doing this sort of thing, and that there may be more...they just haven't found them, yet.
You can have success, but it involves about 6 months to a year of serious lifestyle changes, becoming an entirely different "you" than the one who developed this problem in the first place. You have to completely remake your body...through strict and sweeping dietary changes (become a balanced vegetarian, basically, limiting your access to animal fats and simple carbs common in the Standard American Diet, or S.A.D.), mild detoxification protocols (big ones could shake scary monstors loose in your bloodstream, as opposed to giving them time to dissolve away with subtler means), and only after you've eaten cleany and impeccably for several months, a mild exercise regimen that starts you off slow, and progresses at a super-gradual rate. All under the guidance of your physician, who should be regularly monitoring your blood chemistry, and performing regular dopplars of the identified clot locations.
My Great Uncle died from a thrown thrombosis...too big a heparin shot freed the clot, which was free to travel to the lungs and take him. My sister in law, on the other hand, did the above. No more DVT, and a blood lipid and endocrine profile that suggests she's going to outlive her own grandkids.
If you're serious about beating DVT, you got to get started. It's not a cause, but rather an effect; a disease state that in itself is an effect of over all diet, exercise/fitness, and inflammatory states in the blood as a result of eating SAD foods that your body has identified as bad for it...mild food allergens, etc. I would suggest you get shecked for celiac sprue wheat allergy as a start, and follow-up by reading Peter D'Adamo's "Eat Right for Your Blood Type".
But that's just what I would do if it were me; I can't actually make recommendations over the internet.
Regards,
Dave