Okay, so you probably won’t find anything off the shelf. It’s not common for someone to want to plug a microphone into an aux input. Most microphones are plugged into microphone inputs. But I did some searching and other people have asked the same thing, but without many specific off the shelf solutions.
However, we know a couple things. AUX in is designed to be fed from something that normally powers headphones, right? Because AUX in is there so you can use an audio cable from your phone to play music in your car. Your phone is designed to drive headphones.
So what you need is a microphone amp or other microphone device that allows monitoring of the microphone via headphones. Something like this should work:
Personal Headphone Amp and Monitor Mixer
www.sweetwater.com
Problem is it’s designed for the 3 pin mics used by professionals. I’m assuming you have a 3.5 mm jack on your mic. So you’d need an adapter cable for that. And it’s 12 volt powered so you’d need a cigarette lighter to barrel connector too. But it’s specifically designed to allow headphone monitoring of microphones, so it should work. Simply plug the mic (with adapter) into the mic input, then run an audio cable from the headphone jack to the aux in on the radio.
Bluetooth, well I’m not sure how your 2016 with JBL audio does things, but my 2014 with factory audio (not JBL) is terrible in general at Bluetooth audio. Sounds like crap when I’m on the phone. I struggle to hear calls with marginal audio quality. Since you have hearing issues, I’d avoid Bluetooth based solutions. Even with good setups, the audio quality with Bluetooth is greatly reduced. I had a 2020 Silverado with decent audio and I originally used Bluetooth for phone calls before I started using Apple CarPlay, which is wired. Audio quality on phone calls got so much better when I switched to CarPlay.
That said, there’s no way I know of to link a Bluetooth mic to the speakers, short of Bluetooth mic to a phone, calling another phone that’s connected via Bluetooth to the radio. This is a very clunky solution that would seriously degrade the audio over a wired solution.
I can try to look around some more when I get home later and see if there’s something more plug and play for trying to do this.