Of course, it can be harm to the recovery of your eyes. A cataract is a clouding of the normally clear lens of the eye, which can eventually block the central line of sight and impairs vision. Cataract surgery is an operation to remove the clouded lens. And after the surgery, it is important to have a good rest, so that it can do a good job to the recovery to the eyes. When you do jog, it can increase the eye strain, and lead to some eye diseases. In this way, it can just make your eyes in the risk of emergency. Anyway, just be careful about it. For example, you should not watch TV or computer in the first week after the surgery. And also, pay more attention to the irritants around you, so that your eyes can not be infected.
According to your description, your health conditions are not very satisfactory at this point. Therefore , my suggestions for you is to reduce the amount of physical exercise, and extreme sports should not be allowed because that is quite dangerous to your eyes. As to jogging, maybe you can do it after a period of time of recovery. Consultancy from the doctor would be authoritative.
Of course, you can till your recovery. But you still need consult your doctor. You must keep in mind that do a little exercise is okay. Eating more fresh fruits and drinking some lemon juice which takes advantage of recovering. No smoking and no spicy foods. Take medicines on time under the instruction which was given by your doctor. Keep your eye clean and relax.