Apple watch update and pair issue

So I was originally just trying to install an update on my Apple Watch. I had just restarted it so that I could then update it. After this, my Apple Watch wasn't showing up on the checking for updates section of my phone. I decided to reboot both of them so that they could sync. What this ended up doing was unpairing them. This wouldn't be a problem except it now won't pair the two again, and the phone app still seems to think that they're paired. The watch itself is telling me to put the watch near the phone. Doing that doesn't seem to do anything. The phone is stuck on checking for updates, and the watch is stuck on pair with phone. I don't want to factory reset the watch because I don't have a backup. Both have wifi and bluetooth turned on. The watch is I believe a series 3, and the phone is the new SE.