Not so long ago, I was asked on a thread about using a Frio bag for insulin. I said I would post what kind of a sling bag I use. The one I use is this one:
https://smile.amazon.com/gp/product/B01ALPKQK2/
You can see the shock cord on the top front, which can hold a Frio bag evaporating to the outside with no trouble (best seen on the third pic from the top).
For some reason it shows as unavailable right one – I am pretty sure it will be available again. But, just in case, here are three others with decent reviews that have the same feature:
https://smile.amazon.com/warehouse-Tactical-Shoulder-Backpack-Military/dp/B0188I3YGC/
https://smile.amazon.com/Huntvp-Tactical-Military-Backpack-Trekking/dp/B015QVL6BE/
https://smile.amazon.com/dp/B01MZ2DSH4
This is not our favorite carry bag for everyday gear – a bit too heavy. But it’s the one we use when we need to carry a Frio bag for insulin with us.