Out of IP's - adding another LAN but running into dns issues

Hi all,

I struggle through every step with these routers, very sorry for the noob questions but please be gentle, I don't really know what I'm doing here.

So we were quickly exhausting our single class C network and I decided to run another line from the Fortigate 60E (is that a vlan or a subnet, not sure) to a new switch and give myself another 200+ addresses.  Main net is 192.168.1.0, and I made the new lan 192.168.3.0  I have the fortigate set as the DHCP server for this new segment and so far I've fought my way through to a point where clients pull an ip and can communicate internally and externally.

I can ping from a 192.168.1 machine to a 192.168.3 machine, but if I try to remote in by machine name, it fails, so I have a dns issue for sure.  I have the new LAN dns set to our DC at 1.10

I'm also a little worried about security, as I basically just added policies to open everything up between the two LANs and between the wan and new LAN.

I'll attach a few screen shots of the current config...if anyone has any suggestions or critiques on anything I've setup here, they would be greatly appreciated.  I realize it's a lot to ask, we are all very busy, but I thank you for reading.