I think it is very important to tell him. All of your doctors need to know all of the meds you are taking.

I use Xanax as needed. I am prescribed .5mg but I take less. I have found that most times half or a quarter helped enough. I now use and eighth most of the time. (Sometimes just knowing I have it on hand can be all the calming I need). I have learned if I take that smidgen 1/8th as soon as I notice a feeling of anxiety possibly becoming out of control, it is the pefect amount it to prevent the anxiety/panic from getting worse. It also helped prove to the doc that I would not abuse it. He prescribes it now with refills. At first he prescribed one month at a time. When the one month Rx lasted several months the first few times, he was reassured that I was truly taking it PRN. I also had to watch taking it often at full strength because I found I was feeling more depressed then.
So, I share this to encourage you to consider trying a lesser doses to see how that goes for you.