Do anti-anxiety drugs just not work on some people?

I was prescribed Lorazepam (1 mg) by my oncologist for the anxiety I get a few days before my chemo treatments. She told me to start with 1 pill, and if that didn't work I could take up to 3 at a time (so 3 mg. total). I tried 3 mg for a few days in a row and felt, well...nothing. No relaxation, no alleviation of anxiety, not even tired. She then prescribed me Diazapam (10mg) hoping that trying a different drug might work. I was told to try 1 pill a day at bedtime or when I felt super anxious and see what happened. If nothing, then take 1 and 1 half (so 15 mg). Again...I have no reaction to any of these drugs. I've never used any of these drugs before my cancer diagnosis/chemo treatments. Shouldn't that much of a drug offer me at least some releif? I'm a 33 yr old female, avg. weight, never taken anything for anxiety before this. What could be going on?