strangematters on "Site down frequently with Error establishing database connection, running slow"

Yesterday I found that suddenly my site (strangematterspodcast.com) had gone down and all I was seeing was the message "Error establishing database connection." I'm not sure exactly when this happened but I don't believe I made any changes to the site, maybe updating a plugin the night before but nothing major.

I spoke to three different techs at Bluehost and they all gave different possibilities but nothing really helped. The first guy said it sounded like a database problem, which he couldn't help fix, or to talk to the wordpress side of the site if they might be responsible for the issue. The second tech person got the site to semi-work by disabling all the plugins, which now is the only way I can get the site up but even when it is up it is running extremely slow and half the time still shows the database error message. Not to mention we need the plugins activated for our podcasting!

The third tech guys wrote: "If you get database connection intermittently, the issue could be max_user_connection being used up. This limit is 15 , and gets exhausted if the databases connections made by the user are not closed, and remain open. This is caused by many visitors to the site and activity like file downloads.

So, the fix can be doen by following steps:
1. Uninstall all unwanted plugins.

2. Use additional database users

3. Use a code in your scripts which will close the database connection as soon as the script is executed."

As I mentioned even with all plugins deactivated the site barely works. I created an additional database user but haven't seen any improvement, and honestly have no idea how to do the 3rd option.

He also recommended upgrading to the Bluehost PRO web hosting to solve the problem but I'm wary of giving up a lot more money if I'm not sure if that will even fix the issue.

I have looked over the inteet and these forums and have tried some of the tips to get rid of this message but still have not had any luck. Checked and repaired out database and it says all status is ok. Tried restoring from a date when the site was working with the updraft plus plugin and then later restoring files and database with Site Backup Pro through the cPanel on Bluehost but neither made a difference.

Does anyone have any ideas or can help talk us through how to fix this? I have felt lost and frustrated past two days with no clue what to do. To be honest I am not a very tech savvy person at all, it took me forever just getting a basic wordpress site together for our podcast so with this kind of issue I have no idea where to start. Any help anybody could give would be greatly appreciated!!