MySQL connection timeouts
Inside MySQL, see the GRANTs.  They are hopefully of the form of

GRANT ALL ON dbname.* TO user@'11.22.33.44' IDENTIFIED BY '...'.


Your probably may be solved as simply as copying that and changing the IP address.  Well, change the IDENTIFIED BY part to IDENTIFIED BY PASSWORD('*1234ASDF...') -- the 41-char encrypted password you see in mysql.user.

Note: If you are on 5.7, or have an "authentication plugin" the instructions may be quite different.

Or...

It may be that the OS has firewall protections for port 3306 (or whatever MySQL is using), and you need to poke another hole in the firewall.