Well that's a pretty new one.
When you say your hearing aid uses a normal audio jack, do you mean a 3.5mm jack?
You could simplify the matter and simply use a splitter (3.5mm male to two 3.5mm female) from the audio source. Then plug a 3.5mm male to 3.5mm male cable from one female side of the splitter to your hearing aid and a normal pair of headphones from the other female end of the splitter.
If you already have USB headphones, for simplicity sake, I'd just use a USB to 3.5mm adapter on them. Depending on the quality of the headphones, you may need to get a powered splitter.
Splitting audio sources between two devices is possible but it depends on your audio source. Also by going with Bluetooth, you'd need to make sure you're using a low latency transmitter/receiver, otherwise you'll get latency issues with the two sides matching up.
*update
If you have your heart set on bluetooth, I'd suggest going with this option. Bluetooth low latency transmitter, then a low latency receiver. Then split the receiver with two 3.5mm jacks and use a USB adapter to 3.5mm for the headphones. Then at least all the cables are tethered to you instead of to the computer. These are the low latency bluetooth transmitter/receivers I've used in the past and had no issues with audio/video sync.
Transmitter:
https://www.amazon.com/gp/product/B01N5KKUR0/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
Receiver: (this one even comes with a 3.5mm splitter)
https://www.amazon.com/gp/product/B01LZRB8HJ/ref=oh_aui_search_detailpage?ie=UTF8&psc=1