A few thoughts from me…
You're doing superbly, particularly given you're running on top of asthma.
Something I often want to change with Get Running is the idea of a 9 week plan. In some ways it's great because it's a concrete goal (jogging for 30 minutes) in a concrete time frame (9 weeks). The down side is that it makes people start thinking that if that's not exactly what they do, then they've failed, and they should give up. I'd like it if the App could reach out more and say:
"Listen – you're doing something brilliant. Even after week one you're in a way better place than you were before you started. If you want to run for further, that's wonderful, but if you enjoy running for three lots of five minutes, that's also awesome. If you want to build up more, let it happen. For some people it might be quick, and for others it might take a bit longer."
The App doesn't say that, so that's what these forums are for
I was reading a post on Runnerworld a few days ago. A columnists was responding to a letter and saying that plenty of runners will run for a few minutes and then take a walk, and then run again.
Something else that it takes a while to get is that lots of things influence how much you enjoy a run, and how able you are to run. I had a fabulous run last night, but every run I did last week was pretty rubbish. As you run more you'll find factors that have an influence, but at times it will still seem pretty random and unfair.
So, the summary…
Go easy on your self and be proud of what you can do. If you want to do more, you'll get there. Feel free to dial back to one of the easier runs from last week and do that for a while longer.
One final thought – I think people are often emboldened by their success in the 20 minute (and rightly so), and tend to then pick up their pace in the following week. They don't notice that they're pushing themselves harder and wonder why the running feels difficult, even though it's just shorter runs.
Okay – I'm done

Please keep on going, and I hope you enjoy your next run, how ever long you decide to run for!