Apple Watch Ultra "High Pulse" when Running

False high pulse can be triggered in most optical sport watches if the Watch is too loose, but you need to feel your actual pulse against the stopwatch to ensure it is not for real.

Try the other wrist.

After that if all settings normal but behaviour is irrational there is a progressive hierarchy of remedies...

First force restart the Watch

i.e. press and hold both the side button and Digital Crown for at least 10 seconds, then release both buttons when you see the Apple logo.

 Then, although it may seem irrelevant, while it is restarting Force Restart the paired iphone   Force restart iPhone – Apple Support (UK)

Test it for a while. If it is still misbehaving... Unpair and set up again

 Unpair and erase your Apple Watch – Apple Support (UK)

and then

Set up your Apple Watch – Apple Support (UK)

 If no better you may want to unpair then set up without restoring the backup.

You may also want to make sure the software on the watch and iphone are both up to date.

Update your Apple Watch - Apple Support

Update your iPhone or iPad - Apple Support

If you've completed that troubleshooting and the issue is still not resolved, Contact Support.

 Click here > Contact - Official Apple Support

or phone numbers 

Click here > Contact Apple for support and service - Apple Support