When I click on a link from a Google search, instead of opening the page it searches different engines - what gives?

Based on the appearance of the term “affiliate” in the second link you posted, then I would say yes you do have a virus.

It’s a browser hijack and could be either a virus or adware/spyware type of program.

I’ve seen that “my search” thing before as part of a toolbar (I think).

It’s a very tenacious thing but the last time I dealt with that type of nonsense was years ago. Switched to Mac and haven’t been bothered by that type of nonsense since.

There might be certain PUP/adware on your PC. If my homepage is changed to another one or my search queries are redirected to unknown sites, I will run antivirus program to scan the PC. Usually, a malicious plug-in or extension will be detected. Just remove it and the problem can be resolved. Or you can check the browser extensions and remove the suspicious one manually.