I think reactions to the radio active tracer are rather rare. However, it is possible to have allergic type reactions especially if they used an iodine based tracer. So my answer to your question is yes it is possible.
If you don't want any unsolicited advice then don't read the rest of this post. Shaking, elevated heart rate, and shortness of breath with movement indicate infection to me and possibly pneumonia. You need to get yourself checked out by a doctor.... tonight.
The deer and rabbits are welcome to anything that grows in this yard. Although I did become annoyed when the deer killed the cherry tree by stripping off all the bark on it.