Sounds like you are taking a rescue medicine for asthma. Some people are sensitive to the heart effects of this medicine and get a rapid heart beat, as you do. This rapid heart beat and shakiness that accompanies it is more of a nuisance than a real threat, unless you have underlying heart disease.
That you need to take this inhaler frequently or regularly, is an indication that your asthma is not well controlled and that you should be on one or more long-acting medicines for it. Two that would not affect your heart rate would be an inhaled steroid, such as Flovent® HFA Inhalation Aerosol (fluticasone propionate) or another medicine taken by mouth Singulair® (montelukast sodium). You should ask your doctor about these.
My doctor told me this is a very common problem for people who use inhalers. I guess for now yours wants you to get the benefit of the inhaler and suffer through these heart palpitations. Maybe you'll get used to the inhaled medicine better or later he will reduce the number of times you need to take the inhaler---or give you an inhaler that delivers less medicine and doesn't have this effect. I hope it's better by now. Jane