Large indexing tables crashing site

I have a site with about 188,000 articles. I have started the process of using cloudflare, but maybe that was too late. Now, my site seems to be doing the following and I can’t access the site. Wondering what I can do to make it so my site is usable. This is the message I am told exists from my hosting company:

The process ‘Creating sort index’ are hanging and do not seem to be terminating causing the processes to build up once again. The tables they are referring to, wp_terms and wp_term_taxonomy, are fairly large tables, 238109 rows each.

How can I go in and optimize the databases? Or, is there another fix without using plugins? I am getting a little shy of the plugins.

Thank you for any direction you can share.

The page I need help with: [log in to see the link]