No, acid reflux is not a side effect of taking insulin, but it can be a side effect of diabetes
I have been on insulin for years, but a few months ago I was prescribed Omeprazole for acid reflux and an associated cough. This is the explanation given to me by my GP
We know that diabetes can affect the feet, eyes, and so on, but it can also affect the stomach.
It can have an affect on the nerves in the stomach so that the contents are slower to empty. This causes acid reflux which can affect the throat and bring on a cough.
The fact that you have acid reflux and now take insulin is a coincidence. They are both the result of poor blood sugar control, but are not directly related to each other
I am optimistic that if I make an effort to be careful about the food that I eat, both to control my blood sugars and reduce acid reflux, the situation will improve; and I also need to lose some weight, that must be helpful too
With this in mind I have started to take the advice in the reverse your diabetes books