Hello from JustAnswer. This is Dr. Love and I will be glad to help you today.
It is fine to be active immediately after diagnosis of a DVT, but it would be better to postpone any new exercise regimen. After a month of treatment, it is safer to increase activity levels.
If you intend to use the gym to have a location to walk a track in air conditioning, that would be fine. But if you are intending to implement a broader exercise regimen, it would be better to wait until you have been on treatment for a month.
It is appropriate for you to wear compression stockings. Compression stockings do not directly treat the DVT, but rather are primarily used to help ease symptoms, such as swelling, and to prevent recurrence or complications. If there is a significant amount of tenderness is present and compression stockings are uncomfortable, the doctor may wait until some of the acute pain and tenderness is better before using compression stockings. But if you can tolerate them, it would be appropriate to use them.
If I can provide any additional information, please let me know.
Please let me know if I can provide any further assistance.