my iphone 6s is running very slow after ios 11.0.3

Sounds as though it might be time to get the battery checked out and possibly replaced.

My 5s started running slower and doing random shut-downs, even with a full charge. It began doing these after the iOS 10 update, but since I'd had the phone for for 3 years by then, and it's my only phone for the past 2 years, I figured it was time to get clarity on why this was happening, as it was only getting worse with each update. It was driving me bonkers when traveling and needed Google Maps to guide me (btw, I'm still using iOS 10.3.3) and other apps to help find flight info, restaurants, etc.. I finally took my iPhone to my local Apple store in June of this year.

The tech I saw ran a diagnostic on my phone. One of the diagnostics showed how many charging cycles I'd done and that I only had 63% of battery usefulness/capacity left, even when fully charged... something I couldn't see myself to know that was the problem. The tech said I could either buy a new iPhone (I'm still considering buying an SE for several reasons, but haven't the cash right now) or replace the battery. The battery replacement would be $79 + sales tax and the Apple store could do it right then and there. I decided to investigate it a bit at home and learned an indy shop would likely charge about half what Apple does. So, I called 4 indy repair shops. The shop I went with charged me $32 + sales tax. The most expensive indy shop wanted $48 + sales tax. I could have bought all the necessary parts on Ebay and done it myself, but I was too worried of causing damage to my phone, because my eyesight isn't that great anymore. So, for the extra $10 or $20 dollars I paid, I figured it was worth sitting in the indy shop's waiting room for an hour (I actually went for a walk instead since it was gorgeous day) and letting someone more skilled than I do it for me. SO worth it! Having a new battery totally solved the slowness and random shut-down issues I was experiencing.

I haven't updated to iOS 11.x because I haven't got enough room in my iCloud storage account, and I can't afford to be without a phone, in case I run into any problems.

I also run a VPN on my phone to prevent snooping, etc. too. Yes, it eats up battery charge when it's running, but replacing the battery is much cheaper than buying a new phone.