Any time you start a new medication, any time you put something "foreign" into your body really, you run the risk of having some sort of "reaction" to it. There is ALWAYS that risk. Even with over the counter drugs. No one, not even your doctor, can predict if that is going to happen, as everyone's body handles things differently.
Generally speaking, i haven't heard of many guys having adverse effects from it beyond pain where they got the shot. If your endocrinologist thought it was going to do more harm than good, they wouldn't have prescribed it for you. Keep that in mind.
If it makes you anxious to think there "might" be a reaction, then try to plan to have the shot when you don't have to be somewhere (or do anything) after. That way you can just go home and relax for the day.
I got dry mouth, weird taste, hot all over, and lightheaded after my first shot - i wanted to go home and sleep, i just felt off - but that's mostly because it was a shot, and had little to do with the T. It hasn't happened since. Take what you will from that. It's just my experience.
Any honest concerns should be discussed with the endocrinologist.