Some people can have more of a hyperadrenergic reaction with some medications. For instance, I have been diagnosed with inappropriate sinus tachycardia and then with postural orthostatic tachycardia syndrome. When I have gotten nubain, at times benadryl, chlorepheneramine maleate, and even phenergan, they can cause an increase in my heart rate.
Bricanyl (terbutaline) is a bit different than my albuterol that I use when I need it for my asthma. Both are bronchodilators. Albuteral does raise my heart rate a little and give me the jitters for about 15 minutes. Then it fades but it's a normal effect of the medication.
I read up a little on terbutaline and those side effects are not uncommon either. But if they persist or get worse each time you use the inhaler, you are supposed to contact your doctor. 112 bpm isn't all that fast. Your heart rate probably goes higher than that if you run across the street.