Sassy, explain to her that there is a difference between addiction and dependency. You are dependent on your meds and are under a doctor's watchful eye. If your doctor is a good doctor, he/she is monitoring you and will not give you enough of these drugs that you would become addicted. BUT the key is that you take the medication exactly as prescribed. If you are running out of meds before the end of the month, that is definitely not good. But, if you take your meds exactly as prescribed, or take less than is prescribed, you should be fine.
This explanation might ease her mind. She just loves you so much and doesn't want to see you hurt. My brother was an alcoholic and destroyed himself and hurt all those around him and my heart sinks whenever I see any of my children have a drink! That's what love does to you.