Update issue of Drupal 8.34 Currently, there is a security issue of Drupal CMS, I'm using Drupal version 8.3.4, does the version 8.3.9 can solve the security issue released on March 28th, 2018 PSA-2018-001 (core highly critical release)?

I tried to update to version 8.5.5, but some of the modules did not work after an update. I got the error message "the website encountered an unexpected error. please try again later".
As you can read on https://www.drupal.org/project/drupal/releases/8.3.9 Drupal 8.3.9 fixes SA-CORE-2018-002 (and hence probably also SA-CORE-2018-001). However, there has been several later issues - see https://www.drupal.org/security - and only Drupal 8.5 is supported. Quote from the latest 8.5.6 release: 


  Versions of Drupal 8 prior to 8.5.x are end-of-life and do not receive
  security coverage


In other words, you better upgrade to Drupal 8.5.6 and fix/upgrade the modules that no longer works.