The problem with a gym is that any sound made will go everywhere regardless of the direction it's first aimed. That's why your students can't hear you, because of all the other sounds bouncing around. Adding amplification to your voice is going to interfere with the other teacher making them want amplification, which will interfere with you making you want to turn up and so on. A classic arms race.
On a purely technical level the best solution may be IEMs for the whole class. But as a practical matter the solution may be something other than sound reinforcement (as already mentioned).