This is definitely something you'd want to discuss with your doctor. If they told you no running, jumping, etc., I would follow that advice until they provide different information.
The good thing about weight loss is that the majority of your progress is going to come from what you eat. So even if you can't exercise at all, you can you still lose weight consistently if you're tracking all of your food and staying in your recommended calorie and nutrient ranges.
Hope that helps,