Hello annalouise87 and welcome to Apple Support Communities.
I see you are having some issues with an app called SearchUpdate.
That app is considered to be malware and it's also likely what is slowing down your Mac.
Start by deleting the app which you should find in your Applications folder. Then, reboot the Mac in Safe Mode in order to clear caches and give yourself a good foundation.
How to use safe mode on your Mac - Apple Support
After a safe boot, restart the Mac again normally and test. If you are still experiencing slowness or the references to SearchUpgrade continue, then consider installing and running MalwareBytes.
Malwarebytes for Mac — Mac Antivirus Replacement | Malwarebytes
There is also a good resource with tips for avoiding this kind of issue in the future.
Protect your Mac from malware - Apple Support
Cheers.