Hi Weezer and thanks for the excellent question. While we cannot provide medical advice or diagnostics here (for your own safety), I believe your concern can be addressed without compromising our position.
In the most general of terms, one's heart rate can be affected by many parameters. One of them is hypoxia (low oxygen levels). The body's first response to hypoxia is to increase the heart rate. If one is hypoxic, and it is because of an asthma exacerbation, certainly the heart rate may be increased. On the other hand, if the medication, (aminophylline), relieves the asthma exacerbation, one's oxygen level may return to normal which could result in the heart rate coming down to within an acceptable range.
There are many other causes of an increased heart rate and, I'm sure you'll want to discuss this with your physician to determine what your particular situation is.
I hope this brief explanation has provided you with some additional insight for your concern. More importantly, I hope it will lead you to discuss this further with your physician and let us know how it all turns out.
Wishing you the best, Leon (site moderator)