I have an alarm clock with two alarms on it. The first is radio, at a reasonable volume. The second is beep Beep BEEP with ascending volume. If the first doesn’t wake me the second will. Unless I press the off button and fall back to sleep.

I’m amazed the clock with the bell doesn’t wake you (if you mean one of the traditional alarm clocks with the bells on?). Those things are LOUD.

As sound isn’t working, maybe try one of those “silent alarms” which just turns a light on to help you wake up naturally (I haven’t tried these and would definitely have a beeping alarm as a backup!), or something like a Fitbit which can wake you up by buzzing on your wrist (and will adjust when it wakes you to match your sleep cycle)