How do I clean the hole in my tooth post-root canal? Any tips to keep it clean until I can get a crown?

You shouldn't have a hole. That should have been filled with at least a temporary filling material. If you can't get the crown yet, that's fine, but you need to have that hole filled so the tooth doesn't become infected. To fill the hole may cost a few hundred dollars but it's very important that the root canal material isn't exposed.

There is a temporary cement  you can buy at the drug store. Clean out the hole and make sure there's no food impacted then place the temporary cement on top. It's important to seal the tooth so the root canal doesn't fail. If you can't afford the crown right now, have the general dentist put in a permanent filling.