cant talk about asthma, but I have shot lungs though being a lifelong smoker and 10 years working with fiberglass boats. I've got a severe spinal injury, steel rods in my back, osteo-arthritis and fook knows what else - (basically - totally wanked out ol' hippy)
I have tried eating, smoking, drinking the herb and I always go back to spliffs.
For a non-smoker - try an electric vapouriser. Cooking is easy too but the only ingestion method that I use specifically for pain releif is 5 or 6 spliffs per day.
One way you might like to try is drink your herb. Crush as much dried flower as you can get hold of, into neat vodka, I use at least an oz, very dry - almost crispy. make sure it is crushed as fine as possible. pour 1oz herb into a glass sealable container (eg demijohn) and pour a full 75cl bottle of vodka into bottle and stir. Leave for 2-3 weeks before max potency id reached.
You can now strain off the brown liquid, which has absorbed about 80% of the THC. Drink as required. (bare in mind that the full bottle of tincture contains the THC of about an ounce of best buds.) Keeping a known bud/alcohol ratio allows you to better guage the dose. The residual mud can be dried off slowly and makes a nice light smoke - or can be used in savoury cooking.
Exotic liquers can be used also - like cherry brandy etc - this helps to mask the earthy taste. Or just add orange juice and ice.
Regarding which strain/type is best... well, do you have the luxury of choice right now ? seems to be scarce everywhere.
Home grown buds are top of the list for medication, you can refine your dose in a much more controlled manner when you use the same, known ingredients each time.
For those who have the luxury of bags of skuff - this is a great way of making exotic tinctures and cocktails.