If you use an amplifier with some full power bandwidth in hand, and an adequate output swing to start with, this should not be a problem. Struggling with an LM324 with only a 5V supply, I fear you are on a hiding to nothing. The fact that you may have scraped 3.7Vp-p in one configuration does not prove much. By the time the amplifier was delivering a few mA for the LED and a few more for that zener the level would probably be lower still.
I can't tell you what amplifier to use, as I'm far from up to date with these things. If you wait a while, with a bit of luck someone else better informed may help you out. Perhaps you would also do well to be guided by someone at your school - they may even have something a bit more suitable going for free.
I can't tell you what amplifier to use, as I'm far from up to date with these things. If you wait a while, with a bit of luck someone else better informed may help you out. Perhaps you would also do well to be guided by someone at your school - they may even have something a bit more suitable going for free.