If you have kept track in some manner of the customisations, then upgrading your site version is not that difficult. The way I do it is to first upgrade a clone of the live site and test it completely.
What you have to do is to take the file that is in the upgrade and compare it using one of the file comparison tools to the file on your site. You find where you made changes and copy them over to the new file in the upgrade. You do need to pay attention because the share this code and some others will require you to manually add your change instead of a simple, copy left/right using the comparison tool. I open the new file in the left pane and my current version of the file in the right pane.
I am using the latest mySQL and php versions on my site running Dolphin 7.1.1. I will soon be applying the 7.1.2 upgrade to the live site since it appears to be working on my test site.
Of course you should back up your site files and your database before making changes.