Is core-control still safe for those centOS6 issues?

Hi!
Upgraded my site to the latest WP yesterday & now I’m getting all those errors that seem to come with it:

“You have an error in your SQL syntax; check the manual that corresponds to your MySQL server version for the right syntax to use near ‘TYPE=MyISAM’ at line 9 on line: 1471”
AND
“Warning: An unexpected error occurred. Something may be wrong with www.ads-software.com or this server’s configuration. If you continue to have problems, please try the support forums. (WordPress could not establish a secure connection to www.ads-software.com. Please contact your server administrator.) in /home/debora2/public_html/blog/wp-includes/update.php on line 287”

My server host advised this “is related to the heartbleed exploit that affected specific CentOS6 boards” & relates to WP providing updates over openSSL.

Further, “We do have plans to update all of our machines to the latest CentOS6 release … however in the meantime you might continue to see those warnings, at least until WordPress improves the logic behind the OpenSSL check. …You may try resolve this by installing this plugin https://www.ads-software.com/plugins/core-control/. Once the plugin is activated, load the Core Control settings page and activate the HTTP module and update the plugins that you are experiencing issue with.”

So I installed core-control, but I’m a complete novice & in my attempts to find out how to use it, I came across the advice that it relates to a previous version of WP & is no longer supported.

I just wonder whether I should continue to try to use this, or there is some other way for a novice user to fix her WP installation?

Apologies if this is covered elsewhere: my Support Forum search revealed so many possible fixes I got even more confused…! ??

Thanks in advance for your time.