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The likelihood that you have any viruses on your Mac is pretty close to 0% as there are currently no know Mac viruses in the wild (last I checked). What is more likely is that the AV software you downloaded mistook normal, benign files as viruses. There are other types of malware that can cause problems.
You don't need AV software on a Mac. While you have have some malware on your computer, it's not the first thing I'd consider if the computer was running slowly. To start, I'd look at Activity Monitor and see what's going on. AV software itself is notorious for slowing down Macs.
For more in depth diagnoses, use Etrecheck.
Feel free to post the results here so people can help you figure them out.