Reindexing through phpmyadmin has no effect

Using Magento version 2.2.2.

I have an issue where a product’s price in the search view differs from its price on the product page. The product hasn’t been on sale recently, so I think it’s a reindexing issue.

I went to System -> Tools -> Index Management. It said that Product Flat Data, Product EAV, and Catalog Search all needed reindexing.

When I selected those and set them to either Update by Schedule or Update on Save, the “Updated” date changed to the current time, but it still said “Reindex Required.”

(I have an error at the top of my dashboard that says “One or more indexers are invalid. Make sure your Magento cron job is running.” That’s probably related).

Attempted fixes: I flushed the Magento cache immediately before and immediately after reindexing. And when I set it to “Update on Save,” I added a new product to try and trigger the reindexing.

What do I do to reindex these things properly?