I’m running a Minecraft server on a local PC and would like to have it run through Argo Tunnel and be connected to the mc subdomain on my subdomain. However, when I try to add the tunnel to spectrum I’m unable to add a dns record and don’t have an IP to add, as the pc is behind a university firewall.
You can’t use both Argo Tunnel and Spectrum at the same time.
If you want to run Minecraft server, without additional software used/installed at client side, use Spectrum. You will get an dedicated IP address that can be used directly to connect from MC client. But that requires public IP.
In your case that there’s firewall, you can use Argo Tunnel, but that requires ALL users who wants to play to use additional software on their clients (cloudflared client), which can be tiresome. You might want to check tutorial related to it (https://developers.cloudflare.com/cloudflare-one/applications/non-http)
I don’t know who your target users are (for public/friends or relatives/etc), but I would rather buy a cheap VPS from DO/Linode/Vultr/etc or use Tailscale (similar to VPN, but works on firewalled environments, How to set up a private Minecraft server · Tailscale)