Maybe there is lint or dust in the port and the aux cord has trouble plugging in. If you have a case, try again without the case. What happens when you reboot?
You can reset settings: Settings > General > Reset and tap Reset All Settings.
https://discussions.apple.com/thread/7234451
This worked on iOS 9 aux issues.
Could be that the cords’ plugs just aren't fitting into the jack properly. I’ve seen this issue with 1/8” jacks and plugs for many years…before even iPods were out. Using a blade to trim away a bit of the plastic at the base of the plug worked in some cases.
IOS 10.3 has code in it to disable non MFI (Made For iPhone) accessories. Perhaps your aux cord is not certified.
You may have jumped from 10.2.1 or lower to 11, thus rendering your aux cord useless.
Do you get an 'Accessory not Supported' message?
Well, the only problem is the Aux chords I am using I have been using for years.
I've never seen or heard of an AUX cord getting the "Accessory not supported" message. I thought that was for lightning port accessories or the old-style charging adapters from pre-lightning days.
On that iPhone? I see. The supplied headset is working OK, I presume?