You sound like me--overweight, asthmatic, and have PCOS. Are you insulin resistant? Many women with PCOS are also insulin resistant and that can make it very hard to lose weight. It is definitely something you want to be tested for if you haven't been already. Metformin can help some women with IR and PCOS lose weight, but it's no substitute for good diet (low carb, low sugar) and exercise.
I've had the most luck with brisk uphill walking. Start off gradually, walking slowly on a flat surface for 20 minutes or so, and increase your pace, time spent walking, and the incline of your route as you build up to it. Stretch before and after you exercise to prevent muscle cramps. Be sure to take your inhaler with you in case you overexert yourself, and water to prevent dehydration. You want to build up muscle and to get your heart rate up and keep it there, but not to cause yourself to have an asthma attack. Just don't try to do too much in the beginning because your body has to build up to a steady exercise routine.
I have PCOS and asthma