Running advice: from 10k to 21k with exercise induced asthma?

Hi there,

so currently I can run 10k, but suuper sloow. I did my first 10k race recently, in 71min (which I was quite happy with). On my usual runs, I takes me around 8min/km (with elevation). Here's a typical run: http://runkeeper.com/user/manooh/activity/79750890

I can't really run any faster than that (yet), because otherwise my heart rate goes up to over 180-185, and then my lungs get light asthma symptoms that don't go away for a few hours. And I end up not enjoying the runs if I push myself to run faster. The 10k race really was the upper limit of what I can do without getting asthma. If I try to stay below heart rate zone 4 (= below 167), I can't even run much. I have to walk a lot, which I find quite boring.

Now, I'd love to do one 21k race this year (mid October). I have run close to 20k before, but really super slow, and I had to rest for almost a week after that. 

I'd also like to be able to do 10k in one hour.

What do you suggest that I do? Most running plans say interval training, but I dread the idea. Running one steep hill is enough for me to feel dead afterwards. Pushing my lungs too far usually makes me stop enjoying the runs, and losing interest altogether. I could do intervals while still staying below my heart rate and lung limit, but I'm not sure if there's much of a point doing that. 

I only started recently to run on a regular basis, running around 15k a week. I'm 811rv for about 2 months now (with the exception of one weekend with rice, steamed veges & (unfortunately also) bread). Oh, and I have a Garmin xt 310 now :-)

Thanks in advance,

Manuela