Well your RHR is fine, that's excellent actually.
I'm a male but my RHR when resting (I take it whilst in bed) is usually in the 54-60 BPM range, sitting up its more of 64 BPM usually.
If you're doing really intense endurance training like sprinting than 200 BPM is probably normal, but like the above commenter said, it may not be the best to carry it at that level for a long time if you have any complications from your asthma.
It varies from person to person, but I'd say it depends on what you're doing and for how long you're doing it. 200 bpm is about the maxium rate you'd attain for your age and sex, going "flat out", giving every ounce that you can. This is not a rate that you'd want to carry for an extended period. If this is that case, and say...... you're a distance runner, I'd see a physician to make sure it's safe (which by the way I don't think it is.) One of the problems you could experience is insufficient filling of the ventricles. The leart is pumping so fast, the ventricles can't fill fast enough before it's pumped away. This is often experienced in people with SVT, a condition that produces rates of 200 to 300 bpm. It results in light headedness, and syncope in some individuals.
When I was around your age my HR would jump to around 200bpm when working out as well. See below and if by using this method, you are right on track:
The traditional formula for finding your maximum heart rate is subtracting your age from 220. For example, a 70 year old would have a maximum heart rate of 150.
If though it bothers you, talk to your doctor about it. You may just want to also avoid stimulants such as caffeine etc. I saw a cardio when I was your age for the same exact reason.