I'm sorry you are dealing with a grouchy uterus! Don't we have all the fun?! Yes, I was on terbutaline with both pregnancies and yes, it did make my heart race. It didn't bother me much but I was desperate to keep my babies in so I guess I wasn't too focused on the side effects. I was also on Nifedipene which gave me killer headaches, and I had to take 600 mg Advil/ibuprofen every 6 hours. I credit these 3 meds with allowing my babies to grow to term. I delivered both at 38 weeks.
Hang in there - it will be so fun to hear about your little one!