It's likely you were not getting the fly in front of the fish. There might be other issues too, but first & foremost, the trout won't be caught where they are not.
You need to learn how to "read" the water & determine where the fish might be. In water with current, very different situation than a farm pond, any fish species will be where they don't have to fight the heavier currents. They may be in fast water, but there will be something that breaks the force of the current. They can't fight it & survive.
The fish will also be where they can eat. Generally, they will be out of the current, at least where they need to expend too much energy & where food will come to them. They may be on the bottom, or they may not.
Since that section is not the fly fishing only section, you might consider trying some bait. Heresy for sure! However, I'm not suggesting abandoning flies either. Consider it a learning experience, not about catching, but about learning where to cast. I learned a lot in my youth about fishing currents while using various baits with a fly rod.
In the waxworm case, the spin guys may be catching simply because that bait has scent & they know where to toss it. That's what you need to learn is where to cast the fly.
On a bait versus fly comparison, there may be a weight difference too, so the bait might be sinking at a faster rate than the fly. That would be something you would have to also learn & compensate for when using flies.
You might try a jar of Gulp Waxworms, which keep better than real waxworms. Once you figure out where you have to cast to catch the trout, switch to the flies & see if you can still catch them.
IF, you should succeed with catching the trout on flies, give the fly only section a try, as there should be no spin anglers there.