multiple iCloud sign-in requests?

I have an iPhone 6s that I bought new in September. No issues at all until about a week ago. At least twice a day, I get a notification that I need to sign into iCloud because I've been signed out. This is very frustrating. The only new thing that I have done is I got a new Apple Watch Series 3 (GPS) a few days before this issue started happening.

I have done the following to try to fix the issue:

1) Turn phone off/on

2) Reboot phone (power button and Home button)

3) Sign out and back in of iCloud

4) Changed my iCloud password

None of the above has worked. I know my phone syncs properly with the Cloud when I'm signed in because all of my photos and other items are stored in iCloud when I check on a PC at work.

I DO NOT own a computer or Mac, therefore I can't restore my phone from iTunes.

The phone works fine other than me having to constantly sign in to iCloud.

I'm running IOS 11.1.2

Thanks!