I initially sent a PM here because there were some specifics that I thought deemed discussing. But in following along, I think there are some general thoughts that may be helpful, and clear up some cluttered thoughts/advice. I am a sub-specialist who deals with clot both inpatient and outpatient.
First. The treatment of DVT or PE is systemic anticoagulation. Full stop. The only true indication for an IVC filter is a contraindication to being on blood thinners. There is some nuance and there are special circumstances, but IVC filters when used should only be used as a short-term option. You still ideally need to be on blood thinners, as you can develop collateral vessels around, and they are thrombogenic in and of themselves. Also, as noted, trying to remove them after too long can cause major complication.
Heparin is good in the acute setting as an IV agent. Lovenox is also appropriate. Then Warfarin and the Factor Xa inhbitors (Apixaban and Rivaroxaban) are oral outpatient therapies. None of these “dissolve” clot. The body resorbs clot. But the thinners help prevent more clot from forming, and help in the breakdown or resorption process. There are thrombolytics (clot buster), but this is reserved for absolute life or limb threatening situations.
Warfarin is the old mainstay. It is a Vitamin K antagonist, and subject to labile effectiveness based on dietary changes. Therefore, dosing can fluctuate and it needs to be monitored closely with frequent INR checks. The Factor Xa inhibitors are fixed dose, and much more stable with their effect. They don’t require monitoring. The issue as pointed out is that in general, they are not immediately reversible, so any trauma can be life threatening.
In OP case, a large/extensive DVT can cause post-thrombotic syndrome, which can have long-term consequences. So there is sometimes a role for an interventional radiologist to perform catheter directed thrombolytics. But that is a decision made by thoughtful evaluation and sub-specialist discussion. This also goes for sub-massive pulmonary embolism. But again, requires a highly sub-specialized discussion and approach.
Regarding risks. Clots are either provoked (associated with a risk factor) or idiopathic. Risk factors can be related to long travel and immobility, orthopedic/routine surgery with prolonged immobility, smoking, hormonone therapy (testosterone, estrogen), malignancy (everyone with a clot should be assessed for age appropriate cancer screens). May Thurner is a rare, but anatomical risk factor. Then there are inheritable and, or acquired thrombophilia or clotting disorders. This work-up is complex, does not need to be performed in the immediate setting, and should be done by a thoughtful sub-specialist (Hematologist). Lastly, there is idiopathic, meaning no clear contributing factor is identified. Treatment duration is based on whether or not there is a modifiable risk, or not. If there is a clear clotting disorder, or clot is large/life threatening and idiopathic, then treatment is often indefinite.
Activity level. Many people are very active on long-term full dose anticoagulation. Many people are injured while on anticoagualtion, and there are good stabilizing therapies available. But, obviously, hypervigilance becomes important. Regarding exercise tolerance, everyone is different. If clot is limited to extremity (DVT), then generally want several weeks of stability and tolerance of anticoagualation before attempting to return to vigorous activity. With pulmonary embolism, there will likely be some efffects on endurance, but that can and should improve.
Sorry to have droned on. And apologies for not weighing in sooner. But wanted to provide some clarity to the very informative and well intentioned advice everyone has thus far provided above.
ETA: And what Amnesia said! 