Please check your listenning ports with :
netstat -nat |grep :3306
If it show
tcp 0 0 0.0.0.0:3306 0.0.0.0:* LISTEN
Thats is ok for your remote connection.
But in this case i think you have
tcp 0 192.168.1.3:3306 0.0.0.0:* LISTEN
Thats is ok for your remote connection.
You should also check your firewall (iptables if you centos/redhat)
services iptables stop
for testing or use :
iptables -A input -p tcp -i eth0 --dport 3306 -m state NEW,ESTABLISHED -j ACCEPT
iptables -A output -p tcp -i eth0 --sport 3306 -m state NEW,ESTABLISHED -j ACCEPT
And another thing to check your grant permission for remote connection :
GRANT ALL ON *.* TO remoteUser@'remoteIpadress' IDENTIFIED BY 'my_password';