The "dig" command from the Linux terminal command line does this.
The purpose of a static IP is so that the Pi-Hole will always have the same IP address, then the router and/or clients can be mapped to a DNS address that doest't change. In your router, you would find whatever IP address is used for the Pi-Hole now, and make that static (or reserved, depending on your router).
That should work as well.
It's probably best if you upload your debug log and post the token here. Then we can look at your configuration and see if there is an evident problem.